Mass Effect Legendary Edition crashing in-game post-Eden Prime

UPDATE: OK so after two days of trying everything I or the internet could think of, I finally bit the bullet and decided to do a complete re-install. I synced my saves to the cloud and then uninstalled the whole game from my Xbox, followed by a hard reboot.

Then - having had a lot of weirdness when trying to install the first time around, (because apparently it tries to download the files rather than use the install discs if you're online, even though all the files are right there on the discs!) - I put my console in offline mode and installed the game directly from the discs: first ME1, then 2 and 3 after; keeping an eye on it so I could switch to disc 2 when it prompted me. Once the entire thing was installed, I then put my Xbox back online and let it download the patch, and THEN finally booted the game back up and re-synced my savegame. And... so far, it seems to have worked. No clue if something went wrong with my first install or if I just got lucky this time around, but I figured I'd post something in case it helps anyone else!