After thorough testing with other games, different download locations (hard drive, memory unit etc) I've come to the conclusion that attempting to enter the Download Again window of any of the Fallout 3 DLC I've previously purchased freezes my Xbox 360 completely and I need to restart.
I've cleared the Marketplace Cache, the System Cache, deleted all existing Fallout 3 DLC etc, basically everything suggested in other posts on similar topics. Skyrim DLC downloads fine, New Vegas DLC downloads fine. Only the Fallout 3 Marketplace items are causing my system to freeze.
To be more specific, the process goes like this: I go to Games tab, Search Games, Fallout 3, Extras, All, Broken Steel, then I click "Download Again" and the confirmation window comes up. But it never actually comes up. The spinning progress animation spins once or twice then the whole Xbox freezes. This result is exactly the same with Point Lookout and Mothership Zeta, but no other game DLC gives me this problem.
I've tried going through my Account Downloads History, and I've tried going through the game's own menu. Same result. I can't Add to Queue over this website either.
Is there something about old Fallout 3 DLC that's competing with a new Xbox security update or something?