It appears that my STMUX problems may have gone away. A few weeks ago I loaded a tracing hotfix for Sametime. The hotfix was simply intended to debug the STMUX task. Since loading the hotfix my Sametime server hasn't hung up again. My Lotus Support technician said that about 3 or 4 other customers have stated that after loading the debug hotfix that the problem has gone away.
While it may seem strange that additional debugging may have resolved a problem, consider this. A while back I was having to debug some Lotuscript that wasn't working right. So, I did the usual - throw in a MSGBOX statement to throw a status up to the server console. After adding this the code worked. I had even tried recompiling Lotuscript before that, so I don't believe it was just the fact that I saved and compiled the code. Who knows?
Anyway, I'm pretty hopeful about Sametime being OK. But, I will let you know if I have any other issues with it.
Now it's time to start considering an ND7 upgrade...