Thanks for the tips, Barry. A couple of these guys seemed to know their BMW's, so I didn't bother trying to assist them with diagnosis. They did cut a hole in the tunnel to inspect the linkage and determined that it was either simply a stuck linkage (broken or dropped pin or something) or a shattered synchro gumming up the works. Given that I had NO trouble shifting into 2nd in the first hour, I don't think that synchros were the problem. And I don't think the trans would have lasted another 22 hours with broken metal bits floating around in it. So it was probably just a stuck/broken linkage.
We pulled a trans from someone's DD and had it on stand-by, but ultimately decided it wasn't worth the time penalty of at least 90 minutes (180+ laps) to fix a problem that was only costing us about 6 seconds per lap over the fastest cars.
After 22 hours of almost constant running at 5000 rpm, a few other odd mechanical problems, and about 45 minutes in the penalty box... we finished a happy 19th overall.