You can convert to the AX15 from the NSG370. Since your model year ours the crank position sensor on the right side of the bellhousing, you’ll need the special AX15 bellhousing that Advance Adapters sells which has a place for the stock 2005-2006 sensor to mount to. The factory bellhousing from 94-04 will not have that provision.
Clocking is related to where the transmission came from. XJ Cherokees have the transfer case pattern in the back of the transmission clocked about 10° from the Wrangler pattern. If you buy a brand new AX15 from Novak, it’ll come with the Wrangler pattern, so no cause for concern. Transfer case will slip right on and any input gear your transfer case has should seal properly to the AX15 with no issues. Only a short input gear is required but a longer one won’t hurt either, 99 TJs came with the long gear on AX15s and the AX15 was no different that year than prior.
Clutch parts are the same across all models: the clutch itself, pressure plate, pilot bearing, throwout bearing, clutch fork, fork pivot ball, fork retaining clip, master & slave cylinder assembly. Flywheel is year specific and you would keep the 05-06 flywheel. Before that, 91-04 were all the same.
The only other things to deal with are the transmission to tub interface, i.e. the console and boots. I’d recommend hunting eBay for 5 speed boots, tunnel covers, and console halves until you can piece together something that works.
@mrblaine has done this swap at least once, maybe more, so he can likely help with what’s needed there to make it look stock. A few others have also swapped and just came up with their own boot solution since factory parts are becoming difficult to find. Personally I’d want to find the old tunnel cover and the proper inner and outer boots to match plus the front older console half, but with parts becoming unobtainable, you can only do so much.
It’s a shame the NSG sucks. It has the perfect ratios on paper, but its real world driving experience doesn’t seem to hold up. I much prefer a 6 speed myself, but if it’s junk then that’s not great to live with. Good luck.