Why not just try the short cage RD first. 27T cassettes are usually not beyond the range of short cage RD, though if you have a triple or 50-34
CW then it will not have enough cage wrap. Bent cages may be bent hangers, rule that out as well. Swapping parallelograms involving rivets
and pins will probably require a press or rivet forming tools which can be improvised if you are so minded. There are springs involved hidden
in the works and without an exam it is unclear what the likelihood of parts launched 30' on release a pin might be. Disassembly of the bad
RD should help figure out how easy it will be to do the swap. Might be worthwhile to cruise your LBS for a junked RD for destructive exam
first.