I just saw your post ... I've been using RunGPS w/ A2DP to my Logitech (I think that's what I have) headphones and haven't had ANY cut outs. I keep my TP2 in a fanny pack designed for MP3 players I got on closeout from Best Buy.
I have noticed that the latest version of RunGPS seems to have GPS issues more often
Its odd, because the version notes indicate that it was supposed to FIX issues this the HD2 which I figured would be quite similar to the TP2.
Anyways - A2DP is working fine for me while running. Maybe it is your headphones?
Oh, and I usually use either windows media player or the HTC Sense Player. I like the interaction with the headset buttons (volume, pause/play, skip tracks etc.). I have tried the Mortplayer, but the buttons didn't work (maybe volume did).
Good luck and happy running!
Jason