DIYbanter - floating slab on slope?

Any ideas on how to (cheaply) build a floating slab on a slope, (about
30" drop in 20')?

I'm in early thinking stage of building the cheapest 20x15 foundation
for a shed/garage possible. I'm in uptate NY, so frost can be a problem
(42" frost depth reqd). The site is sloped along the 20' length,
dropping about 30". There is a little room in the back to slope things
down those 30" behind the shed, but I don't want to extend a slope out
for more than a few feet. The shed only has 3 walls (4th wall is big
swinging doors), and I don't care much about the floor material.

My stupid idea was to dig (by hand) 12" down in the back (and the full
42" on the sides, I suppose), and pour three walls with a footer, then
fill with whatever fill material I can find cheap.

Talking briefly to the helpful inspector here, he suggested a
floating/monolithic slab sitting on a big pile of gravel "bank run" or
stone fill. Or, if I'm a little nervous about that 30" steep bank in
the back, I could put just a single wall in the back, and tie it in to
the slab with the three remaining edges thickened, as usual. I'd only
need to dig down 12", and I suppose have to do two pours (one for the
wall, one for the floor and remaining three edges. The wall build have
to be buried on all sides anyway, to get the 42" frost depth.

Is this last idea, slab-tied-to-wall crazy? Or even necessary? How
steep a alope would be too steep to manage without any kind of
retaining wall? Any way to do this all in one pour instead of two tiny
pours?

Or the real weird one: would a mixed foundation (one part footer+wall,
three parts floating slab) be a bad idea due to differing frost action,
or different movements, etc.?

Thanks as always.
-Kevin