OK, my mistake on the legs. Quartersawn, yes, but solid. No rays and flakes on all four sides. I sanded the bottom of one of the legs.
Impervious to DNA, so some petroleum distillate is my guess. I'll go out and hit the top with DNA and see how it comes out. If it cleans up nicely, I may just put on a sheet of plexiglass or maybe tempered glass, though glass would cost more than the table.
Water dissolves the glue, so it's hide glue.
I'm not sure that I want to completely dismantle it. The gaps are big enough to dissolve the old glue with Q-Tips and water. It's going to sit against a wall with my desktop computer on it. I hope- I haven't checked it for clearance with a chair in front of it. Might not be ergonomic enough.