My thoughts:
Whilst not beholden to the MEL as you mentioned if the failure occurs after dispatch, I would still consider the FL350 restriction valid. I can only imagine it is a ventilation issue.
If on a flight where cabin crew rest was required, I would liaise with the cabin crew to try to get them to start (and therefore finish) their breaks early, maintaining max FL350 whilst that was occurring. Also, although unpopular, minimise their breaks to the legal minimum. CI 0 and other mitigations to ensure the fuel penalty for non-optimal levels was minimised. Once breaks completed, then I would step climb. If 3 pilot ops, I wouldn't have a problem with OFCR as there would only be one pilot in there at a time and it's designed for two so ventilation would be less of an issue (I would probably sleep with my head at the entrance end though!)