Oscillating vibration around 60-70 mph in 6th gear

Check for DTCs diagnostic trouble codes. It may be a misfire under load. It could also be any of these.

https://truckomize.com/f150-shakes-shudders-when-accelerating/

It appears to be a known issue and your question is famous already :>D

https://www.google.com/search?q=2017+Ford+F-150+has+shudder+or+hard+vibration

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A full rotation and balance couldn't hurt. Possible brake issue too...

Sounds liike a ring and pinion on rear differential. U can pull the cover off and check this or another thing would be to check your u-joints.

That is a typical RPM at that speed for most 6-speed 4 cylinder engines. The reason for this is that they have a much lower power output at lower RPMs (due to lack of torque), and the engineers want for you to have SOME acceleration to get up little hills.

check the "u" joints for looseness and wear especially the front drive shaft . check sliding splines . The vibration is a harmonic vibration normally associated with worn "U" joints --bent or out of balanced ---worn /seizing slip joints or being excited by a failing drive thrust bearing in the diff. ( big bearing directly behind the pinion gear that takes all the load on drive) check the magnet on the diff drain plug for metal bits.

you may have a bearing in the trans that has failed allowing the main shaft to sag

Based on the info you gave, I would say the engine is experiencing a miss-fire. At some point it should be bad enough to set a code for the cylinder or random missfire.
I would check the plugs and the ignition system first. The engine is working hard when it goes into overdrive at a low speed. Any minor problem will show up then.
The O2 code could be important too, if the fuel system is running lean. It takes more gas when the engine is pulling hard.

Try reading the codes if none found then check the fuel line pressure it should be 55lbs

Often as an engine ages and parts wear out rhythmic oscillations can cause a obvious and repeatable noise. Even when new, hitting a resonant frequency (for my personal car holding at 1500-1600rpm causes a terrible noise and vibration) If you're only experiencing sound as a result of the speed it is probably not a major mechanical issue. However, I have had a car before, about the same year as this one, where as it tried to shift gears at about 40mph into fifth gear the engine would bog down, detect low engine speed at prepare to downshift, and would repeat this process. Solution to that was cleaning the fuel injectors (which will run you about 50$ most places.)

check for loose engine / trany mounts