OSDev.org

I think that I would use like freedos, and then some dos extender to get into pmode with full ram access.
That way, your program basicly owns the computer and you still have the 32-bit benefits. It would also easily fit on a floppy.

Maybe not the answer you would expect in the 21th century, but my OS (that would suit you perfectly) isn't "finished" yet.

how does one go about getting such an extender?

If you're really just wanting a small linux with a replacement shell you might want to look at the Linux from Scratch docs.

I've never actually used one, but I do have some Google skills:

http://dos32a.narechk.net/index_en.html
http://www.thefreecountry.com/programmi ... ders.shtml