You might want to do some more diagnostics before doing your swap. (Bear with me here.)
The AW-4 (all years) is an electric controlled transmission. Without the functioning transmission control electronics, a brand new transmission won't shift properly. I want to say the manual mode for the AW-4 is, 1,3,4 & R, no torque converter lockup, no second gear, no automatic function.(That's from memory, not the FSM)
From what you're describing, it sounds more like an electronic failure then a mechanical failure. If that's the case, changing the transmission won't fix the problem. As it all died at once, I'd look at the TCU, wiring harness, and plugs at the transmission before I pulled the trans. Unlikely to have both shift solenoids blow at the same time. Also check for power to the TCU. In the 96-back models, the trans system is on a separate harness, and doesn't "talk" to the engine control computer.
"Never attribute to malice that which can be adequately explained by stupidity, but don't rule out malice."
My other car is also a Jeep,.. and so is the other one,.. and that one too. How many do you own before it's "a herd" ?