I've determined that the WINEDEBUG trick for getting around the mousclick issue is unnecessary. The debug process slows everything down (as stated before), but also is the cause of the instability.
Turns out, if I just open the PChat launcher several times, eventually one will let me click properly. If I'm lucky, it happens within the first round.
On a related note, I think I learned this lesson early on, with Island Rum (.exe version) when logging into the Homecoming servers. Eventually I can use mouseclicks, and I've never had a stability problem.
-S