95 YJ with 3-speed auto has trouble getting into 3rd gear

Unfortunately swapping in another non oem trans would be cost preventative as opposed to having yours rebuilt. Should it have held up longer, sure , but I dont think you'll find to many people praising Chrysler built automatic. Doing a manual swap is probably more reasonable but still the AX5 is not considered a HD trans. My 91 runs 31's has a 4 and AX5 and it has 150K on it now and works just fine for trails and highways at 70. I will admit I rarely use 5th gear though.
 
How loose is your kick down cable? Try tightening it. Have you serviced the transmission fluid including filter? Doing these may make it feel less like ol’ yeller
 
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