The ideal thermal solution is a combination of both of those ideas. Foam on top of the existing roof is a good way to eliminate thermal bridges, provided no cold air is allowed under it. The roof foam should be held down with 2x4's laid flat and screwed into the rafters with a layer of plywood over that, then the new roof. Doing that plus filling the bays with cellulose will vastly improve your insulation situation. If you do the foam on top of the existing roof, keep in mind that the attic above the flat ceiling is now within the heated envelope, so the small gable walls will need to be air sealed and insulated.

Bob had it right- putting foam over the roof deck (+ sealing the soffit/ridge) is superior to spraying insulation from below, in that it protects the roof deck from thermal & moisture cycling. It stays warmer & dryer during the winter. With enough exterior R, you can then fill the rafter bays with cheap fiber for a higher total R. In zip code 18976 you're good with anything more than 25% of the R value as exterior foam from a wintertime condensation point of view, which would make the average January temp at the structural deck ~ 41F, above the dew point of 70F 35% RH conditioned space air.

You didn't specify which type rigid foam, but at 3-4" ANY foam would be sufficient R to be able to protect the roof deck even with fiber insulation between the rafters. but EPS (bead board- usually white) would be the cheapest per unit-R, and 4" would deliver ~ R15-R16, which would deliver ~R35 total if combined with spray cellulose (~ R20) between the rafters. If they're talking polyisocyanurate 4" would give you ~ R22.5 (figure on an aged value R5.6/inch in a cold-weather roofing application, even if R6-6.5 is the 75F rating.) and you'd be over R40. The labor cost of 3" is the same as 4", the extra thickness adds another R4-R6, depending on the type of foam. Code is probably R38 for new construction in your neighborhood, but R50 can often be rationalized if you have higher-priced heating fuels.

Using 2x furring to hold the foam down might be overkill in your climate- it depends on the actual roof pitch & anticipated snow loads etc. (The shallower the pitch & deeper the snow, the more vent cavity you need.) Be sure to screen the venting at both ends with critter-proof/bug proof screen or you can end up with a squirrel-condo/bees-nest-central in those cavitys. With 4" goods and 2x furring the screw lengths to secure it to the rafters can be cumbersome, raising installation costs, which may affect the foam thickness and choice (3" of iso is slightly more R than 4" of EPS.) If you rarely get over a foot of snow accumulation on your roof, and have R40 or more of insulation you can probably use 1x furring on ~4:12 pitches or higher.

You can also use OSB rather than ply for the nailer-deck to save a bit. The nailer deck isn't structural so it's ratings don't have to be particularly high, and being bottom vented you don't have nearly the rot risk that can occur with OSB flat on the foam with felt & composition shingles above trapping snow-moisture in the nailer deck for weeks/months. Taping or foaming the seams of the rigid foam is also worthwhile as a secondary air/moisture block for the structural roof below.

2X may be overkill for an engineer looking only at the numbers, but I'm thinking of the holding power of nails holding OSB to 11/16" (typical actual dimension) 1x3 strapping. The combination of screwing through the 1x3 to hold down the foam, plus nailing the OSB to strapping with ring shank nails, plus the roofing nails which will penetrate the strapping could cause the strapping to crack. I'd stick with 2x4's.