It fails with this log output in the dev console, and a message "A fatal error has occured, this connection is termianted" on the screen, and then it takes me back to the server choosing screen.

Try deleting your config files and ensuring the mod is correctly installed.

I received the same failure to load with this log: http://pastebin.com/SGEHiHKP
Upon removing Inventory tweaks, this log: http://pastebin.com/6pV2eRiy

This is on loading from single player world selection, still sends me back to the server selection screen.

Deleting the config/mod and replacing it did not work.
Forge version: 10.12.0.1039
InventoryTweaks-1.57-dev-110

Edit: I am using 24 mods total in this instance. With just Forge and Inventory Tweaks, I can load the world and play on it. I will be adding each mod individually to pin point the conflict now.

Edit2: Results of individual mod rule-out test: http://pastebin.com/WZvR1Z3s
BoP is the conflict at present.

Edit3: Hadn't realized there was a 112 build, same result (with all 24 mods loading): http://pastebin.com/aiaJcdGU

Edit4: reported it to BoP: http://www.minecraftforge.net/forum/index.php/topic,17204.0.html
I don't know what's actually causing the problem, so I wanted to make sure I told them too.