This is possibly the reason why there was no early hand-over (between FOs) up to the very last moment (as the actual PF was the most qualified on type onboard). Hence, the very late hand-over could be simply due to the junior FO and Captain switching seats (and I fully agree that it would be some kind of desperate move).
takata, please consider what TLB posted in re whose body was found in the initial search and recovery, not strapped in a seat. I had forgotten that fact.
From TLB:
I do not think that we can assume that the Captain took over the LHS prior to impact. Given that the Captain's body was recovered floating on the surface days after the accident, and that the two copilot's bodies were apparently recovered on the ocean floor still strapped into their seats, it seems unlikely that the Captain got into the LHS.