I've tried running the patcher twice now (the first time installing directly to my clean Fallout New Vegas directory, the second time installing to a separate folder and doing a manual install) and both times the patcher has not included the Fallout3.esm file with everything else. It is the only file the patcher seems to have a problem with, even The Pitt works absolutely fine. I tried using the unmodified Fallout3.esm file from my Fallout 3 directory and, unsurprisingly, I CTD'd immediately when starting the game.
I don't know what I'm supposed to do here. I can't find anyone else who has ran the patcher and experienced this issue. I've ran it as administrator both times, so I know that's not the issue. I've included a screenshot of the directory I installed TTW to the second time, taken after the patcher finished running. As you can see, Fallout3.esm is nowhere to be found.