I'm not entirely sure what happened, but as of last night, I have been able to play without a single crash for about 2 hours WITHOUT disabling the internet connection. In fact, I even got to play some Team Deathmatch online for a little bit. Rather goofy, but I'm not going to complain!
It again suggests that the server problems that GTA has had are related to the single player problems and that the internet connection plays a big part in these issues.