If you submit a paper-proposal to one session (meeting) at the MLA and it is officially rejected, is it kosher to submit that same proposal to another session?
Yes, I think that would be fine.
Often abstracts are rejected less because of the quality of the work and more because it doesn't fit with the rest of the panel.
The difficulty is that the deadlines tend to be very close together--usually March 1 or March 15. It would not be okay to just double submit the abstract.