If I misheard "ABC 1234 TCAS climb" as "ABC 1237 request climb" (and I think that could be most easily done), I would come back with "negative maintain niner thousand"... if I believed there was traffic above. Aust AIP says "TCAS RA..." which I have heard a couple of times (both false alarms obviously, I'm still in the business) and really got my attention.
If an ATC has still not yet grasped the situation, the pilot is supposed to respond to any such instructions with "UNABLE TO COMPLY, TCAS RA (thinks: f%$#wit...)", or something like that.
Follow TCAS for vertical, and ATC for headings
Sounds like a dumb idea. On the other hand, if I have compromised separation and think the TCAS is possible RA'ing as I speak, (heaven forfend), I would issue an alert and a suggested heading and not screw around with the levels. I would leave the levels to the TCAS.
If nothing else that should tell the crews that the guys on the ground have bolloxed it up and trust your technology
