Thanks for the suggestions!
Well, reading other threads and blogs was what made me choose the bamboo batting, which I'm wondering if that's what's causing the bearding. If I stitch with the needle and no thread, there's no bearding, so my guess is it's not the needle? The red and orange threads so far seem to be the worst, and the yellow seems to be ok, but it's also entirely possible the fibers just show up more against the red and orange! It's always worst on the first stitch after I've buried the knot.
In all the reading I've done on big stitch and perle cotton, no one talks about waxing the threads or using thread conditioner. So odd! I didn't expect to have this issue.