I found a bug in usbbuffer.c in the TivaWare USB library. The symptom was that, during bulk HOST IN transfers, an incorrect byte would be transmitted every N bytes, where N was the size of the transmit buffer on the TM4C.
I narrowed it down to the ScheduleNextTransmission function. I found the way it was written confusing, so I refactored it, and lo and behold, the bug went away. (Which technically means I didn't refactor properly, since I didn't preserve the faulty logic...)
This is for revision 2.1.2.111, although I didn't see any changes in the release notes for 2.1.3 so I suppose it is still valid.
If anyone's interested I can post the refactored function.