Best to dig straight down to the footing with more than 2" (3"+ is better) but to save money use EPS (Plastifab is available at HD, not that I like to promote them), then go out at least 2' horizontally if you can. It will work well. You don't need to do under the footings if there is none under the slab (or even if there is, it's a bit late).
Are you going to heat this space only when you are in there?
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