Well, my plan of winding up the facial control lines with bolts (threaded through nuts in the top) didn't work at all. Not sure what the hell I was thinking. Of course, when you wind the string on the bolts, there's no tension to keep them wound. They just unwind. As well, the mess of hardware and strings and the trouble of tieing strings among a mess of hardware makes it unworkable.
I solved the 'attaching lines to the latex' problem. I tied the line to a tiny little washer, glues that to a little piece of latex, and then glued that on. It stays good enough, but they can be torn off (making them repositionable and test-able). Once established in their final spots, i'm going to coat them in latex to really bond them on there.
I did find a solution to the first problem though. Sort of.
The above picture is the top of the head with a pool of resin, to fill all the unneeded test holes.