Well it seems like I've got this fixed. After a bit of faffing (removing the tuner, disassembling the tuner, incorrectly reassembling the tuner, re-disassembling the tuner, re-reassembling the tuner), I discovered that the "ear" and the stem ARE, in fact, separate pieces, and it seemed to be the ear wiggling in the stem, rather than the stem moving in the thread, that was causing the problem. Didn't seem to be enough room to slide anything between the surface of the ear and the slot in the stem, so I just squeezed the stem with a pair of pliers and this seems to have done the trick! Sorry for wasting your time everyone, but the effort's much appreciated all the same!