I thought I had already written this update, but it looks like I didn't. Score one for early onset senility, I guess.
I dug the little cape fragments out of the rubber the other day, and lets just say it was not pretty... for the most part. As I suspected, the only fragment that fared well was the one that I put the clay around. The one that was taped down stayed taped, but the rubber stuck to the fabric around the edges. While the rubber did peel away, it left some discoloration, and little chunks of rubber in the material.
The piece that was free floating was a total loss. Rubber seeped all the way under it, and totally impregnated the fabric. Same as the first square, I was able to peel it away, but not without leaving little chunks in the fabric, and a bunch of discoloration.
But the good news is that the clay really worked well. nothing seeped under it, and it didn't leave any residue on the cape.
So that's what I'm going to do. Run a border of clay around the cape, and then go from there.