I'm in the process of building a 2,000 Sq ft 6x8 D log home in the mountains of Colorado at an elevation of ~9,040' I have a full ICF walkout basement with radiant tubing in the slab. I'm looking for cost effective insulation for my 2X12 stick framed roof, 2 X 6 shed dormer framing and 2X4 gable end filler. The log gable ends are 8/12 pitch and the shed dormers are 5/12 pitch so the framed 2x4 walls fill in the gap. I have ruled out fiberglass batts. I'm looking for cost effective ideas for insulation. I don't care about low VOC's during installation, but I do want something that will not outgas after it cures. I would prefer a do it myself approach but it all boils down to cost vs R value and sealing properties. My location is on the cold side of the valley so I have violated rule number one take advantage of the sun. The advantage to my location is the creek that runs trough my property and more importantly much less wild-fire danger than the dried out sunny side of the mountain. 

Any Ideas out there?

Log homes present mechanical strain issues over seasons that stick framed do not due to the expansion/contraction of the logs with humidity & temp.

Closed cell foam may seal well on day-1, but is more likely to develop separations over time (particularly on the gable-ends) if your place is as dynamic as most log homes. Open cell foam might be flexible enough though. If you're looking at a cathedralized ceiling in the dormers, a combination of rigid-foam above the roof deck and open-cell foam or dense-packed dry-blown cellulose on the interior is a good approach, with o.c. foam or cellulose on the gable ends. Rigid foam above the roof deck is a real performance enhancer, in that it provides a thermal break over the structural members and raises the average temp of the roof deck for lower condensation & rot risk. (The ratio of exterior/interior R may need to be tweaked for the local climate to rule out roof deck moisture issues better.)

Going with 2" of closed cell foam on the interior of the roof deck everywhere and filling the cavities will cellulose, with vapor-retardent latex (an not poly or foil) as the interior vapor retarder is pretty reliable, which would give you R50-ish in the 2x12 framed sections. The foam becomes the "condensing surface" that can't wick moisture into the roof deck, and the cellulose redistributes any moisture from condensing conditions on the rafters, buffering it safely until spring (as long as it's air-tight to the interior). Venting the exterior of the roof deck by adding a non-structural nailer deck for the roofing separated by 1x furring protects the roof deck even further by giving it a decent drying path to the exterior instead of spending the winter under snow-covered shingles with zero exterior drying capacity. You could even add 2" of rigid XPS (R10) or 4" of rigid EPS (R15) above the roof deck and below the nailer and still retain some outward drying capacity.

You get a lot more R/$ with closed cell foam, but even more R/$ with cellulose. While not quite as good at air-sealing as foam, dense-packed cellulose shifts and moves with the house. Cheaper still is wet-sprayed cellulose, which is lower density an even less air-retardent (though WAY better than batts), but still quite flexible. As with the roof, exterior rigid board can buy you a real performance boost, even though the flexing of the house could make using gable-end rigid foam as an air barrier less plausible in the long term (but that's what housewrap is for, eh?)

With the vent gap under a metal roof you'll still have good drying capacity toward the exterior.  If any/all sections are to be unvented, study this document carefully, or put a decent fraction of the R above the roof deck as rigid foam.  Unvented with exterior foam can be an excellent option.  Up to 4" (R15-R16) of unfaced Type-I EPS above the roof deck is sufficiently vapor permeable than mounting the metal roof on purlins rather than tight to the foam preserves the exterior-drying capacity by allowing for ventilation above the roof deck, but below the roofing material.  EPS won't wick any leakwater down to the roof deck, and only a semi-permeable drain-plane material need be used between the foam & purlins.  One could go higher R on the exterior with 4" of iso (~R23), but due to the low vapor permeance of the facers you'd be required to design your stackup to dry only toward the interior. (Still not a bad option.)  Also note that at cold temps (say ~20F average temp across the material)  the R value of iso drops 5-7%, but the R value of EPS increases 10-15%, so they're not as different in cold/very-cold climates as the rated values at moderate temps might imply when it's only part of the total R.  (Figure ~R18 for EPS or ~R22 for iso when it's below zero outside, if the rigid foam 1/3 of the total R value or less.)  Cost wise the EPS will be much cheaper per rated R.

Foam seals well, but closed-cell foam isn't very flexible, and depending on how much strain you get it separations over time.   The movement of the logs can/does apply various strains to the roof, not just up/down at the soffits.  The design can limit, but not eliminate those loads, but analyzing whether they're within the elastic limits of closed cell foam over decades isn't something amenable to a web-form.  Open cell foam also seals well, but is far more flexible than closed cell, and probably WOULD handle the strains.

Wet-sprayed cellulose has water-activated adhesives to keep it from settling over time, and is more flexible still. It's air-retardency is quite good from a heat loss point of view, but would still require air-tight methods to be applied to the roof sheathing and interior to keep moisture transport rates well controlled.  In a cathedralized ceiling it can be applied "blown in blanket" behind a purpose made mesh.  It could also be "dense-packed" to 3lbs+ /ft³  to achieve high air-retardency and a somewhat higher R than you'd get with half-pound open cell foam, similar to the R value of 0.7lb Demilec (a somewhat higher density open cell foam.)  Dense-packed wet-sprayed cellulose is likely to be cheaper than open-cell foam, and adds significant thermal mass, which can make it outperform foam thermally at equivalent R value in areas with large daily swings in temperature (such as the mountains of Colorado.)  It can also buffer quite a bit of moisuture without losing R or degrading over time, protecting both the rafters & roof deck. (It's a PITA if you get a major roof leak though since, it will redistribute and hold a heluva lot of liquid water.)  You can get somewhat higher R by dense-packing some of the noo-skool fiberglass blowing wools such as JM Spider (which also has a water-activated adhesive) or Certainteed Optima (dry-blow only) to 1.8lbs density using similar methods, but at lower thermal mass and no moisture buffering capacity (but no soggy mess to clean up & replace should the deluge occur.)

R16 EPS on the exterior and wet-spray cellulose blown in mesh on the interior, with the roofing mounted on purlins and vapor-retardent latex primer on the interior as a partially breathable vapor retarder would give you a low-cost ~ R55-R58 in the 2x12 raftered sections, and ~ R35 on the 2x6 raftered parts.  If you needed more R on the sections with thinner rafters to match, skip the vapor retardent latex and double-up the EPS.  (With 2/3 of the R on the exterior for those sections the roof deck stays well above the dew point of the interior space air, and won't accumulate winter moisture, so let it dry toward the interior- no vapor retarder required.)  If you want to protect the roof deck further, use 1-2" of closed cell spray  polyurethane foam on the underside of the roof deck before applying the cellulose.   The closed cell foam acts as a non-wicking vapor semi-permeable condensing surface in this application, and adds another R2.3/inch above filling the space with cellulose. 

With a less-permeable foam than 4" of EPS on the exterior and without the ventilation gap between the foam & roofing you'd likely either NEED the interior closed cell foam, or make the exterior foam something like 35% of the total or greater, assuming your average January temps are comparable to say, Leadville.  But with EPS with venting above you can avoid the expense.  Closed cell foam is over a buck a square foot for every inch of depth- a premium product at a premium price, to be used judiciously.  It's very useful for controlling moisture dynamics when applied properly,  but can be an expensive disaster if used randomly.

To get decent R values out of 2x4 wall framing on the gables/dormers you can put in 3" of closed cell foam (~ R24), but if there are racking forces from the you may end up with seasonal separations defeating that.  Alternatively you can use wet-sprayed cellulose (not blown-in-blanket, for lower cost), and 2" of exterior XPS rigid board over the structural sheathing for slightly better performance (since the XPS forms a thermal break over the framing.)  It's cheaper and similar performance to go with 2x6 24" on center (same lumbercost & strength as 16" o.c. 2x4s , fewer boards) and go with spray cellulose with 1-1.5" of exterior XPS.  If possible with your dimensions, use exterior vertical furring to give a "rainscreen" ventilation gap between the sheathing and the siding similar to what you'd have on a vented roof deck, to enhance drying toward the exterior. (Make sure it's vented both at the bottom and top of the furring channels for maximum benefit.

Loosely stuffing fiberglass in the expansion gaps for the logs isn't a great solution, more of a "better than nothing" solution.  If possible put a flexible air-barrier (Tyvek or something) loosely enough to handle the dimensional changes without ripping on both the interior & exterior sides of the gaps.  This will limit what would be a serious seasonal air leak, and preserve some R-value for the fiberglass.  (Without air-barriers on both sides low density fiberglass dramatically underperforms it's ASTM C 518 test ratings.)

I couldn't find a spec for ProTecht  but since it's made of 2-layers of polyethylene it's vapor-permeability is likely to be too low to use on the exterior layers in a cold climate such as yours.  It's probably a true vapor-barrier, and suitable only on the interior, if anywhere.  Tyvek is HIGHLY vapor permeable, but a good air-barrier, allowing good drying capacity, whereas ProTecht would keep wintertime moisture inside the assembly on the cold & condensing side to create mold & rot conditions.  Do NOT use it on the exterior.