I quit using Them because the belts kept snapping, and I went to something else, but I bought a bunch of old rubber singer belts one time to run My wrap motor. They are the type that look like O-rings. Each pack came with a larger size belt that I used for that, and a smaller one that I never had a use for until this. They are fairly thick, so They have quite a bit of elasticity and seem to work well. My thinking Is It may work similar to using the surgical tubing to clamp billet, or points with.
It's hard to tell from your picture, but It almost looks as if the glue is wicking back into the darker colored wood. I don't know If sealing the faces before a final thin facing with the tool would help or not, but may be worth a try.
By the way, If your pins went in first, and the glue were already set on that, then You could make a joint cap type thing out of delrin to clamp the joint work while the glue sets. My pins go in after the joint work is installed so I have never tried that, but have heard of something like that being done. I do have something similar that I do using some clamps that I made, but I use those to align & glue ringwork together before going into the cue with It.