My answer to the TCAS question was to climb because it would be within the rights of the PIC to consider this an emergency situation to which I was told was the correct answer.
I have flown on at least two aircraft where I have been aware of maximum altitudes in which there can be a TCAS Climb RA. At least one of them was below the aircraft maximum certified altitude.
In one of those types which was a turboprop, I have also been in a situation on a hot day where it was a big struggle just to get to our cruise altitude which was below the maximum TCAS Climb RA altitude. If you are going to climb at this altitude in response to an RA, be very cautious that you don't end up in a stall situation. In most cases, the other aircraft should have a coordinated descent so usually they will be avoiding you as well.