So I took the desk apart and stripped the paint. Oddly enough, this entire desk was built without a drop of glue (except the top). Screws, nails, and other hardware held everything together. This made it pretty easy to pull everything apart and salvage for future use. Here is what I think I have:
Legs: 4 in decent shape minus a few small cracks that I should be able to fill with epoxy.
Aprons: The rear apron is still a pretzel, but otherwise OK. Side aprons look fine. The front was actually three smaller pieces nailed together, and probably not of great value for much else.
Table top: A solid piece. A few cracks on the edges, mostly along glue joints. There are some significant scratches across the face that will take a bit of work to get out (see picture).
The plan ahead—I am going to try to build a desk similar to what I had previously planned, just using parts from the old desk. Even though the rear apron is a pretzel, I should be able to slice a few pieces of laminate out of it to create a veneer. I will most like just use a piece of the Macore I bought for the rear apron (close enough, and no one will ever see it). The new desk will have a few curves in the front and sides, and will require cutting down the top a bit. The old desk was a little bit bigger than we actually needed. The picture below is a copy of the sketchup plan.