It shakes when gas is applied at speeds above 60 mph-more on some roads than others, and sometimes when accelerating even at lower speeds

Do a test with tranny in drive instead of OD/over-drive, does the problem go away? If so I think it is an OD issue.
Check motor mounts and suspension. In the past, I've seen bad shocks cause a noticeable vibration at a certain speed. Below or above that certain speed, no vibration.

Your tires are either need balancing or you have a broken belt in your tire

Might be the throttle position sensor.

You have a random misfire issue follow the link for info on this problem. Problem 6 Engine Stalls Misfire Code Cylinder Misfire

if it does not go away over 60 and does not shake too bad at lower speeds sounds like your drive shaft is outta ballance if you do any off roading you may have bent it hitting an object or could be something like the diff joints worn or broken shaking it with your hand will tell you that (should not move)

and remember you got 4wd so you have Two drive shafts

hi can you have it scan for a dtc code to know what the problem is or you can buy a diy scanner to do it your self

This may apply. ...............................

Carry out the adaptation drive cycle road test:

Note: This process must be carried out in normal mode (not sports mode). On a flat road, the transmission fluid temperature must be above 60° C (140° f) and below 100° C (212° f) (vehicle at normal operating temperature will ensure that the transmission fluid temperature is above 60° C (140° f)).
9. Accelerate from rest with light throttle (do not exceed the upper rev limit in appendix 1). 1-2, 2-3, 3-4 shifts must occur with engine speed between the following limits:.
Note: Do not move the accelerator pedal during shifts.

• 3.0L VIN ALL 1800 - 2000 rpm
• 4.2L N/A Prior VIN M96321 1450 - 1600 rpm
• 4.2L N/A From VIN M963221550 - 1700 rpm

10. Continue to accelerate gently to 50 mph (80 km/h) so that transmission shifts into 5th gear.
11. Go into overrun and let the transmission shift down into 4th gear without braking.
12. Brake gently to a standstill and hold footbrake on for at least 15 seconds.
13. This process should be carried out at least five times.

Page 2 of 3 Bulletin Number S307-17
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Most likely with this problem is the front tires. The tires maybe " out of balance " or " out of round " causing the vibration at certain speeds.

Well even though you had the rotors turned, they still could be warped and causing the car to shake at a high rate of speed when the brakes are applied. My suggestion is to replace the rotors asap.

what you describe may be castor wobble and is from incorrect wheel alignment
check the steering tie rod ball joints and other suspension items