I liked the TCAS question so did a little search around. I have some slides from Airbus on TCAS which includes the use of RA for Emergency Descents, OEIO and Ceiling.
Here is the slide on this type of event:
• AC 20-131A defines the maneuvers that the aircraft must be able to perform.
• In particular, the aircraft must prove that it can respond to a TCAS RA CLIMB order, even when it is at its maximum altitude.
It referred to this
Advisory Circular
Here is a snippet:
An aircraft's climb capability when operating at or near its maximum approved operating altitude is also affected by excess thrust and true airspeed, which may be available to safely trade if needed for climb rate. Climb RAs should not be inhibited if the aircraft has adequate performance available or because it may exceed its maximum certificated altitude by several hundred feet during an RA.
Also you would have the 1.3G buffet margin at your ceiling so as long as you don't try and snap off the elevator with an aggressive climb, you would be ok?
On our aircraft, we only see the red bar of MMO at FL450 but I have seen pics of the Global with a proper coffin-corner on their speed tape, wouldn't fancy an RA in that situation (or an emergency descent for the same reason).