Re: Whats the most stable transonic bullet?
I'm not sure what help this will be to you, but it might be worth looking at the bullets used by long range black powder shooters. I haven't gotten around to actually doing it, but a while back I was asking questions about the old 45-70 round and how anyone managed to hit anything accurately with it at extended ranges, when clearly it was going to go subsonic less than half of the way there.
Apparently certain bullet shapes are much preferable to others, and a quick search would probably turn up the top contenders for you. Obviously they are very large bullets, 450gr at the low end, and they don't start out very fast, but they do start out above the transonic zone and quickly transition into it, and then through to subsonic velocities, within the first several hundred yards of thier flight.