Well I solved it, although it's likely unrelated to why it hit you, Hunger. But I'll elaborate just in case someone else runs into it in the future. I certainly wish I'd realized it sooner though!
It turns out it was because I wasn't using one of the default bodies. I didn't have any mods installed, but I did use the savegame editor to change my appearance to that of Trask. I suspect (and I'm just guessing here) the problem may be that Trask's model doesn't display headwear. This never affected anything in the normal game, it was actually nice since the silly looking visors and such wouldn't show up, but I think it confused BoS when...
...BoS rigs you out in Revan's outfit including mask.
Even if this isn't the case, it definitely is because I wasn't using a default character model. I went in to my save just before the crash, changed it to use one of the defaults, and viola, that scene loaded just fine. Additionally, I tried setting the save game included with BoS to use the Trask model and it crashed at the same spot. So this was completely my fault and not a bug in BoS.
I've confirmed that it's
Revan's Robes that were clashing with the Trask model. It turns out that the Star Forge Robes cause a crash as well. So this issue had NOTHING to do with BoS.