If you're blocking the cantilevered bays at the foundation with Thermax there is no rationale for a ventilation gap between the subfloor under the bay-window bump-out and the fiber insulation (if there ever WAS one.) A nominal 1" skim-coat shot of closed cell foam (you can use the 12 board-foot FrothPak kits from box stores, if it's a small enough area) on the subfloor would be sufficient vapor retarder to allow you to just fill up the space with fiber insulation, so long as the bottom sheathing of the exterior overhang doesn't have any strong vapor retarders like poly or foil.
On the fiber insulation, both density, and snugness (preferabably a compression-fit) count. I personally prefer to use rock-wool, which is about the same cost & R value/inch as "cathedral ceiling" batts. It's probably not a huge area, so there's no real savings by to going with low-density batts, which are much better mouse-nests. Are they 2x10s, 2x12s or... ???. If it's more than arm's length it can be awkward shoe-horning in batts (especially if there are nail-heads interfering and catching). It's easier to get a tight fit with blown fiber, but it's probably not worth the hassle & expense of renting a blower.
Then, just blocking it in with fire-rated Thermax and sealing the edges (with 1-part can-foam or FrothPak) works.
Where there is poly on the exterior of the foundation, unless you have a metal-flashing or membrane type capillary break between the concrete and foundation sill it's better to use something more vapor-open than XPS on the interior. Using 1.5-2" of unfaced EPS (not the goods with poly or foil facers sold at some box stores, which are <1 perm) would give it 3-5x the drying capacity of 1" XPS for about the same or better R-value. If XPS is all you have available, hold the line at 1" (which runs ~0.8-1.2 perms, typ.).





Now that I am replacing all of the fiberglass that is up against the rim joist with Thermax (inspector won't allow unfaced XPS), but I won't be able to reach in far enough to install this on the protruding rim joist in these two areas. So, my question is, how should I insulate in these areas? Do I need to use spray foam? Or replace the unfaced bats with paper back ones? What about the air flow that appears to be currently in place; is this important?
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