It felt like the longest 48 hours of my life, but I waited two full days before removing the tape and clamps. What a relief it was to find everything holding together and no exposed edge. There's even an overhang of a fraction of an inch into where the original binding strip used to sit in a few spots.
I started slowly cleaning out the rabbet edge with a sanding band attachment on my Dremel. After about 40 minutes, I had made it all the way around. There are a few high spots, and a few places in the joints at the that I'll fill in with some wood and glue, but most of it is already fairly close to where I want it to be.