So, with a little help and shoving from
neferde, a lot of help from the ReactOS IRC room, and a willingness to toss out several dozen gigs worth of replaceable data?
I can rescue my data. In fact, barring one partition I don't have room for right now, I have rescued my data.
There are three things this experience has taught me.
1) If you don't have the money to buy a backup solution, you don't have the money to buy a computer.
2) The list of things I'd be willing to delete wholesale in an emergency is larger than I had known.
3) Frozen chops should be in the emergency kit of every good tech.
I am going to marry those people. Srsly.