Climb authorization
RF4 at 2502: it has been stated many times that his increase in FlL request was denied. It's highly unlikely that he would initiate a unauthorized climb to move up to optimum .
And Lost in S at 2515: He had been cleared to FL340 but there was never a response to that clearance. That tells me they never heard it. It also tells me they did not respond because they were already too busy dealing with the problem that caused the aircraft to climb unintentionally.
It is wrong to simply assume that 8501 did not receive the climb authorization, based on lack of acknowledgment. The clearance may have been received, and pilots therefore may have known that a climb was then allowed, but THEN got busy and were not able to acknowledge. The time bits are small and important.