the 4500 is too big for the application. you'll never need that much tranny. Plus the tranny is about $4k. call high impact driveline and get their nv3500 conversion kit. I is a complete kit for $2200 including the tranny. Then you just need the drive shafts. That is what I'm going to next. For the time being I have a rebuilt ax5 because I didn't have the time or money at the time mine went. If you rebuild locktight the fifth gear cluster pack and you won't loose fifth gear again.
'Too big' and 'never need'? Well, that all depends on what you want to end up with. If you're thinking about doubling down with ultea low gears and big meat then it might be fine. Also, if you're wanting to setup the drivetrain now and then eventually swap engines at a later day, it would make sense to do it. You just have to decide your path ahead of time or else you'll be paying for things twice later on down the road.
Also keep in mind that you can get a NV4500 for around $1800 for the transmission alone. Not $4000. Then $5-600 for the adapters and you're looking at only $200 difference from a NV3550 swap. The only downside is that the NV4500 is heavy, very heavy and it's big, but you'll probably never need to worry about it again. Although if you're not going to go with really low gearing or an engine swap it's all moot.
If the Jeep is mostly and you're not rockcrawling then I'd just swap in a salvaged AX5 and call it good.