Cooling it down faster is not a factor any insulation type can provide, since the primary determinant of how fast it cools off is the total thermal mass and the beginning & end temperature differences. The insulation type doesn't affect the net thermal mass by even 1%.
Ductless AC only hits it's super-high efficiency averages when it is sized correctly to the peak load and allowed to modulate with the varying load. If you want to cool it off quickly to use it for only a few hours at a time you need a larger oversizing factor than is optimal for ductless to overcome the stored BTUs in the thermal mass of the slab/framing/gypsum board/etc. For your described occupancy patterns in the 16' x 30' garage bay, a 15000 BTU point terminal AC (PTAC) in the wall probably makes more sense than a mini-split.
If the 12 x 23 attic room is going to have a similar occupancy pattern, a PTAC makes more sense there too. Even a heat-pump version of a ~15000 BTU PTAC runs less than $800 per unit ($1600 for a pair, maybe $2K all-in if you count the wall sleeve, breaker, and wiring), whereas a 2- 2.5 ton mini-split worth owning would run $3K or more just for the hardware, and would have more installation labor & expertise to deal with. (One such series is the DigiSmart PTHxxxx: https://www.ajmadison.com/ajmadison/itemdocs/PTH074G25AXXX_specs.pdf . LG has a similar series, there are others.)
For insulating the walls, R13 fiberglass is fine, as long as you pay attention to making the framing air tight to the sheathing in every stud bay with a bead of polyurethane caulk (including a bead between doubled-up top plates). With any batt job you need to do an A1 job of fitting the batts to near perfection, tucking in the edges & corners to ensure contact with the sheathing, then tugging out lightly until the fiberglass is just proud of the stud edges everywhere, to ensure contact with the wallboard everywhere when it gets closed in. Split the batts around any horizontal wiring, don't compress them behind the wires, and use a batt knife (or a bread knife) to sculpt around electrical boxes.
For any roof or attic insulation, blown cellulose is more effective than fiberglass due to higher opacity to infra-red and higher air retardency. In your climate you'll want a minimum of 9" of cellulose if open-blown on the attic floor between joists (11-12" is better). If the attic room is going to have any sloped ceiling it may add complexity, but it's still do-able.
If build it reasonably air tight with R13 walls and R30-R38 attic, unless you have a lot of west-facing window the actual peak loads are going to be about a half-ton to 3/4 ton for the garage depending on the outdoor air leakage and the R-value & solar orientation of the garage door. An uninsulated west facing garage door might push the peak to the 1-ton range, but not until the late afternoon. With an R30+ top the attic room is going to come in under a half ton peak, unless it has considerable window area solar gains. With those loads it'll still take awhile for a 15,000 BTU PTAC to bring the temps down 25F (say from 100F to 75F), but probably still under an hour, depending on just how much thermal mass it has to pump down. |