With the 360, you've got to find a way to hang the front diff/axle. 4.0 or 4.0 stroker has the flange for that.
I too would be strongly suggesting you take a look at a 4.0 or a 4.0 stroker. And there's a wide range in choices in doing that. And it's a more modern engine, better balances available between performance, performance choices, reliability, parts availability, fuel usage and emissions. Cheapest quality way is buying a stroker pre-made. More fun to build your own, but usually a lot more expensive, even for the same end result for the low-end crate 4.0 strokers. Do a lot of research. (I didn't, and I paid 4x over what a crate 4.0 stroker costs, to have my 258 rebuilt with 4.0 head, cam, etc.; I got exactly what I wanted, but a crate 4.0 stroker would have more power, more torque, with lower fuel use, etc.. Only extra beyond drop it in, is drilling and tapping for the diff/axle supports.)
As for more mechanical, the NP128 is the only Eagle transfer-case that doesn't have a viscous ring inside to fail and contaminate the TC and ruin it if not caught in time (and where do you get a replacement part, vs. a replacement TC). I ran an '81 with the NP119 in it; loved it - great driving feel. When I got the '86 with the NP128, same, until I was immediately disappointed with it in the first snow - until I got snow tires. I still have an upgraded TC in mind, but with good tires, I've had it over 15 years and somehow an upgraded TC just hasn't been a nag. With on-road, if not slippy surfaces (or you get good tires), if not giving it crazy upgraded HP/torque (see below), I believe the NP128 is the way to go. And you've already got one. Check it over (fluid debris? wear? seals?), and if good thoroughly drain it, fill it back up with ATF+4. (Might want to do the drain & fill twice a month apart if you didn't like the old fluid, so the residual fluid gets diluted and mostly flushed with the 2nd change. A flush is an idea, but I don't know what would do that without residual flush fluid compromising the new fluid; after a few days, a second drain & fill?)
Depending on the HP and torque you put in it, you may need a beefier TC. (and diffs?) NP242 is fine, you don't need the hummer version. If you're only going to drive on-road, and no steep mountains with a trailer, etc., if you got a TC with high-low, you wouldn't be the first person to not have a control inside and leave it permanently in high. The NP128's vac high-low shift 'motor' may or may not be adaptable to other TCs. There's also other TCs than the Np242 that are beefier than the Eagle TCs.