Isn't the 4X4 linkage on the T-case? Are you swapping that too? It should work though.
The shifter config should be the same, the NP 231 doesn't see the small push to the side that you need to do with the YJ shifter Vs. the straigh up pull from the TJ, it's all the same motion to the T-case.
Put the NP 231 from the BA onto the AX15, if it's the NP231 AMG there will be one less bolt than the NP231 JP
but it will fit.
I hope I understood/answered your question.
You're never to old to have toys!
'90 YJ, 4" RC Suspension lift, 1" Shackle lift, SYE and CV, Holley Carb, 33/12.50/15 Dynapro M/T's. RIP my old friend.