It seems like you’ve done a lot of the typical troubleshooting steps already, but let's see if we can dig a little deeper.
Check Wheel Alignment and Balance Again: Even if you've had multiple alignments and balancings, it's worth considering that after a lot of repairs, especially with suspension bits, a follow-up alignment is often necessary. Sometimes shops can miss things, so a second opinion might be worth it.
Inspect the Control Arm Bushings: You mentioned upgrading the upper control arm bushings, but how are the lower control arms and their bushings? Worn control arm bushings can significantly affect handling and stability.
Look into the Steering Stabilizer: Since you've replaced a lot of steering components, a worn or leaking steering stabilizer could also contribute to the symptoms you're experiencing.
Check for Loose or Worn Components: It might sound simple, but sometimes a small loose component can cause a chain reaction of issues. Check all your suspension connections again to ensure everything is tight.
Check the Frame and Body: You mentioned that the frame was inspected, but if you can find any signs of damage or misalignment, specifically around where the suspension components mount, that could be an issue.
Drivetrain Issues: Since you’ve replaced driveshafts and axles, ensure the drivetrain components are well lubricated and there’s no binding or play in the differential. Also, a torque converter or transmission problem can sometimes cause handling issues that manifest as bouncing or shaking.
Tire Size: Running mismatched tires could potentially lead to handling issues, especially with the difference in diameter and tread. It's essential to match all tires.
Weight Distribution: Ensure you're not carrying extra weight or any modifications that could affect the weight distribution, which might exacerbate handling issues.
If you can share any more specific symptoms or odd noises, that can also help narrow it down. Additionally, a video of the bouncing or shaking while driving might help those with more expertise identify the issue more easily.