Leave it in 4A and u don't have to do anything.
If you leave it in 4A, the system doesn't do anything until AFTER wheel spin has started. The system responds to a loss of traction by using a clutch pack in the center differential to transfer power to the front axle and (in the 3.73*) by using another clutch pack in the rear differential to transfer power to the other rear wheel.
There is no way for the system to predict "it's going to be slippery here". The best you can do is for the driver to tell the system "it's going to be slippery here", which is exactly what the drive modes do.** But it's far faster and easier for me to just press the rear locker button and be done with it.
Back to the OP, from a functional perspective, he's really swapping an LSD for a lockable LSD. I don't think he'd have any issue unless he tried to put in an actual limited slip rear differential.
Note that the reactive nature of AWD systems is one of the things that has hampered their adoption by the serious off-road folks. Early systems in particular were known for very rapid transfers of power from the slipping wheel to the one(s) with just barely enough traction. The result of the sudden application of power to a wheel with very little traction is a loss of traction in that wheel as well**. It's not usually a big deal at 25+MPH on the street in rain, ice and snow because your momentum will carry you through to where you have more traction. But when you're doing 3mph up a muddy/sandy incline...
*The 3.23 in the OPs rig does not have a clutch pack in the rear differential and so transfers power to the opposite rear wheel by activating the brake on the wheel that is slipping. The system doesn't know which wheel to brake (nor how much to apply) until one of them starts to slip. And all the literature I've seen calls it an "electronic limited slip rear differential". Which very strongly implies the braking-based-transfer never attempts to match the rotational speed of the half axles but instead merely limits the difference in their rotational speeds.
**In the 4A only systems, this simply changes the bias/loading of the clutch pack in the center differential, but it doesn't lock the rotational speed of the output shafts.
