Type-II may be good enough- how deep is the soil going on top of it?
Under slabs Type-II is definitely good enough.
Backfilling with
shredded EPS &/or low density EPS blocks is a fairly standard practice for insulating over the footings of
large foundations/buildings and retaining walls.etc. Shredded EPS or loose EPS beads eliminates potential lateral frost heave loads by absorbing the mechanical strain, and drains very well. Putting landscaping fabric &/or a heavy vapor barrier (sloping away from the foundation) over the EPS back fill (under 1-3' of topsoil) should work pretty well. Unless you'll be putting a driveway over it, any density shred, Type-I or even loose EPS beads would be good enough for backfill. It's customary in commercial applications to mix the shred with sand to limit potential settling/compaction but that would be less of an issue here. If you take a EPS-shred backfill approach there is no point rigid EPS directly on the top of footing- you'll get a huge R value out of just the backfill even at ~R2/inch (R24/foot.)