I've had two or three cars with posi traction.
Yes, it will wake you up if you haven't driven one in a while.
As a daily driver it shouldn't be hard to "get use to it" and always be aware of conditions... second nature.

I'd that trutrac is a helical lsd......get that.
I don't see a locking member, but I'm not familiar with the product. I went from stock to spool to elocker on my wheeler.
I don't touch domestics, so I'm not familiar.
If I come across a helical lsd for my tundra, I'll put it in. Mostly street rig. Helical lsd is the best option for that.

Here is a good video:

In my first Wrangler (92) I hand Randy ring and penion put true track front and detroit locker in back 4;56 ratio on gears. Loved it.

Yeah "standard" helical. I'd go with that. The only downside to a helical is if one wheel has zero traction like it's off the ground. Then they just go straight open. There are some that have a slight amount of friction plate between them so there is some load but generally if 1 wheels off the ground it still doesn't work. That's fine for a street car but they don't do a whole lot on trails. If it's on road 99.99% of the time that would work just fine. I'll probably end up going that route with my Tundra

Test it as I described with it in gear and both wheels off the ground. If it has a worn out limited slip (I seriously doubt it, most Cherokees don't have LSD contrary to what others here are saying) the wheels will still turn opposite directions but you may feel some resistance. If it's an open diff (most likely) they'll turn opposite directions with only a little drag from brakes, bearings, and inertia. If it has a good limited slip or locker, you won't be able to turn either wheel more than a small amount by hand.

For the uses you describe, it's probably not worth going with either one. Nobody I know who's owned a TrueTrac was very happy with it. Installation of either one requires setting up the differential gears again, which is not a beginner job if you aren't familiar with it. That Chrysler 8.25 requires a special tool for adjustment; you can make your own if so inclined but will need some fabrication skills and equipment.