I didn't see Dave's and Marc's suggestions until after I did the deed, so I didn't do it exactly as you suggested, but it seems to have worked. I soaked some wash clothes in hot water, wrung them out lightly, covered the limbs, and wrapped the whole in plastic wrap. Let it sit like that overnight. The sinew was nice and soft, so I wrapped it in plastic wrap and really tight ace bandages for several hours.
(The plastic keeps the bandages from sticking, Dave. Works really well. How, oh how, did our ancestors get anything done without plastic wrap? Or zip ties???)
Everything looked a lot smoother, more transparent, stuck down really well. Let that dry for a day, and yesterday put on another layer. I had a space heater going in the room so the glue didn't set up so fast, and took some extra time to really smooth out the sinew, removing any twists. Wrapped that up with plastic/ace bandage overnight, and unwrapped to cure this morning. Seems to have worked nicely.
I plan to let that cure for a week, then add a strip down the middle to mound it up just a bit, then one more full layer and a snake skin. Let that cure for a good month or two before I start tillering. As Tom Petty said, the waiting is the hardest part...