Screw everyone that says turbos will have lag. Only if you are stupid and size it wrong.
I come from a Turbo Dodge background(mid 80s early 90s turbo Chryslers) which have the 2.2/2.5 turbo motors, ranging from non intercooled(T1), to intercooled(T2), even DOHC Lotus/Maserati cylinder heads(T3), and VNT, or the variably nozzle turbine(T4). Yes Chrysler had it first as far as I know.
The down fall of these motors(other than the rare DOHC), is that they flow poorly. The 2.5s w/ the smaller Mitsubishi turbo(on non intercooled cars) spools stupid fast, runs a little out of "breath" but honestly, with no turbo it would be even slower.
On a Jeep I see that as an advantage. Take a smallish size turbo(not sure exactly, I would need to see some compressor maps and stuff) and make it work well from 1800-4000 rpms for a modest 6-8psi w/ alcohol or water injection(works better than intercooling, and no intercooler to get heatsoaked while crawling through rocks or get gunked up by mud). Would it give you crazy freaking HP numbers? Compared to a stock 4.0, yeah. The TORQUE is where it's at. I'd guess 360ft-lbs of torque wouldn't be too hard to do.
I would keep compression where it's at and be happy with low boost so it still works with good response when not spooled and also to not weaken the "engine braking" abilities.
One really cool thing about turbos is how they spool up harder/faster when they are under a higher load. That means if you're bogged down in something and need more wheelspeed, give it hell and the turbo will spool and go apes*** and hopefully get you through.
The only really bad thing I heard in this thread that hadn't crossed my mind was dunking it in water. Definitely something to avoid.
Something I haven't found yet is how to tune it. I would want some kind of software to tune on-board w/ a laptop and wideband sensor/reader to see what's going on w/ A/F ratio and the like. Or there's the old school ways of adding a 7th fuel injector and have a diode wired in so it starts squirting under boost or use a rising rate FPR to add 1 psi to the fuel rail for every 1 psi of boost. I'm not sure how the computer would respond to that, hopefully someone can help me out.
#1 - No one really said it'd lag. The 4.0L is huge in comparison to most turbo motors. Damn sure big enough to spool a turbo at low-RPMs.
#2 - A turbo that runs out of breath on a 2.5L would do that much more quickly on a 4.0L due to the exhaust flow, etc. For example... I come from the import world of the turbo realm. 300ZX, 3000GT, etc. (We have 2 of the bastards on these cars.) Turbos that would normally add beautiful top end to a stock 3.0L 6G72, will begin to choke on a 3.5L 6G74 upgrade. Will it make the power? Sure. But eventually, they will just make heat instead of building power due to the flow restrictions. But, like you said... sized correctly, there's no reason why it wouldn't work. I'm guessing you'd be needing something in the TD05 range.
#3 - That alky/water injection system would be a pain in the *** to keep up with constantly and the kind of environment that would be friendly to the turbo, would not have any sort of mud reaching high enough to gunk up an intercooler. Keep the sprayer, but use an intercooler. Hell, with the power level we're talking about, a small side-mount would work just fine. Again, wishful thinking would probably be around +100HP to the wheels.
As far as tuning and the whole rising boost pressures, etc. You would probably need at least one hell of a piggy-back, but I'm guessing a stand-alone would be needed to tune it like you're talking about. The stock computer has *nothing* programmed into it for controlling the FP for boost, or anything to do with boost. Add into that, bigger injectors for the application, and you would probably run into some problems as RedRock experienced.
IMO, supercharger, stroker, or engine swap. The things these vehicles are put through are not turbo friendly. It can be done, by ALL means. It just isn't a very practical idea.