My dearest friends,
I would like to proudly announce to you that this incredibly annoying issue has finally come to a close.
In combination with the very worn differential bushings, the tire size differences in wear made all the difference in the end. Those bushings definitely needed replaced, and drastically reduced the front end vibrations, but the main cause of the issue actually boiled down to the tires themselves. Since I got these tires before winter, I never needed to use 4WD on paved roads, and when I used it, it was at low speeds on the trails. I never would have guessed that the issue actually resided in the ratios in which all of the drivetrain must maintain.
Without a nearly 1:1 front to rear rotation ratio for the tires and driveshafts, the transfer case struggles to output the same speeds with the tires under load and rotating different distances. This, in turn, likely caused the front differential to behave strangely, with the driveshaft and axle shafts not exactly cooperating at the same speeds, causing harmonics to shove the differential back and forth on the bushing mounts, wearing them faster and causing the terrifying vibrations.
With the tires properly rotated, as to maintain a proper ratio as close as possible between the front and rear differentials, the issue vanished. The spider gears in the differentials put up with the fractional differences in rotations between both sides of the front and rear, allowing the power to be distributed properly and everything to rotate evenly. This, in turn, also fixed the transfer case shifting issue. With the front tires matching the rear tires in speed, the transmission-like setup of the transfer case can sync up the speeds and properly engage and disengage on the fly, without damaging anything.
HUGE thanks to everyone that cracked down on this issue with me. As stupid simple as the conclusion was for this, I think it teaches me a lot about how important tire wear is, and possibly teaches us all how far the limits go for our vehicles and their gear tolerances. I'm just thankful that I limped it around in 2WD all winter instead of gritting my teeth and hauling it around while it was shaking, as something was likely to break.
I hope this thread sticks around, this should be very helpful for anyone out there with the same issues!