What are my options for saving this building?
Ultimately, I decided to save it.  I used stacks of cribbing with large beams to jack the building up off of the failing foundation walls.  Similar to this (much larger) example:

Once I had it up on the crib stacks, I was able to remove the jacking beams, pour concrete footers/piers, and set 6x6 posts.  The building now rests on those posts and sits firmly.  Once closed up, it became a nice storage space.