Thanks for the details.
Step one with the vehicle off the ground use a nylon tape measure and measure the circumference of all tires. On an AWD vehicle your highest reading needs to be only a 1/4 inch difference from the lowest reading. If its greater this will cause the transfer case viscous coupling to wear out. Since it is trying to make the front and rear axles go the same speed. One tire larger around than another means the gear ratio will be different because a tall tire will travel farther than short tire if both are rolled one revolution.
Step two drive around 45-55 mph swerve aggressive but safe to see of you get a hum noise that comes and goes. If so then a wheel bearing is bad.
Step three, if there is a transfer case issue, drive with the front driveshaft removed. If the concern is gone, then the concern is related to the AWD system.
Step four drive slow and in tight turns like in a parking garage, if you get a binding, chatter, vibration, groan, moan type noise then suspect the rear axle limited slip clutches in the rear differential binding and grabbing to much.
For the harsh shift have the intermediate and overdrive bands adjusted externally then service the fluid. If it continues then replace the transmission solenoid body.
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