Update: Got it working! In the end this seems to be a launcher issue. Here's what I did, in case it helps anyone:
1. Removed my The Sims 3 folder from My Documents. I put it on my Desktop.
2. Set up the game to bypass the launcher.
3. Once it was set to bypass the launcher, I found I had to double click the icon for the base game. Right clicking and choosing open won't work for some reason. Double clicking gets the game to load.
4. I started a new test game to make sure everything was working, once I was confident it was I moved back in my saved games from the TS3 folder I put on my Desktop.
5. Once I was sure my saved game was working okay, I moved my DCCache and DCCacheBackup folder back into the newly generated TS3 folder in My Documents (when I bypassed the launcher all my store content disappeared from the game, this got it back).
I did A LOT of finagling with the screen resolution in my Options.ini file, but once I got the game to load I changed it back to default then manually adjusted the screen size to 1600 x 900 and the game has been loading fine. All is well for the time being!
