Can i bung and XT rear derailleur on my santa cruz in place of my knckered SRAM X9 without changing the shifters?
The SRAM has so much play in it, the springs are slack and the jockey wheels insist on seizing every chance they get.

no.

different actuation ratio

I found that with an X9 mech from a few years ago I could prise open the seals and regrease the bearings that one of the jockey wheels had. That seemed to eke a little bit more life out of it. I think that the jockey wheel that used a bushing could be disassembled and cleaned a bit too.

I can't offer any suggestions about the play though.

New X9 is a lot different. Different jockey wheels and slimmer profile.

I am about to take a set of SRAM Rocket shifters, that work with Shimano mechs, off my bike. Email me if you might be interested in them (for just a few quid).