Of course, within 10 minutes of posting about this I try to load the game again and it starts up with only a minor delay as if nothing happened. Even has my old save files. The only thing I did differently in the meantime was to try loading another game in Steam just to see if it would work. Something tells me the fix is not for everyone to just load KOTOR and then close it out immediately, but yet my game is working this very second. I guess I'll update if it stops?
Thanks @SnakeheadMonster for the reply. I'm still getting the crash report the majority of the time I try to play the game; I've been able to get it to run twice since Saturday. I tried both "NOSPLASHPRELOAD" and disabling the savegame sync, but that didn't seem to make an impact.
Once again I appreciate the suggestions, but when I disabled the Intel graphics card my computer struggled mightily (multiple crashes). I'm using a laptop and assuming that whatever resources the NVidia card was using to run the display must have put too much stress on the system overall. I did go to the NVidia Control Center and set the game to run only using the high performance card. Unfortunately I'm still running into the crash report more often than not, but at least when it does load I'm able to knock out a few missions at a time.
