I have a free AX-15 5spd transmission- useful?

Good luck with that BA5, Peugeot is not known for making anything good and the BA5 is probably the worst thing they ever made, right next to cars with 3 lugs per wheel. The best thing to do with a BA5 is keep it behind the seat of your Jeep so when the E brake doesnt work, you can use the BA5 to put behind the tire and keep it rolling away. The fact they are about the size of a Stanley thermos makes them handy to keep behind the seat. I would start with an NV3500 and then AX-15, third choice would be to just shoot yourself in the foot because it will be less painful that dealing with a BA5.
The AX-15 will hold up behind a V8 in mild applications of 300 HP and lower, the NV will handle closer to 400 HP. The NV had better ratios and if you can find the close ratio version its even better.
OP, The AX-15 will work fine as long as you arent running big tires and lots of torque, Its the 1-2 shift at heavy throttle that kills them, you end up putting 2nd gear out the side of the case.