They'll tell you to do a flush because that's plug and play for them. Very little labor. Always follow the money.
$700 for the RDU/PTU for what is less than 30 minutes of labor and $60 in fluid is highway robbery.
The tires you had limited your traction significantly.
Source: me, with a couple thousand miles of "off-road" use on forest roads in all kinds of conditions.
In the 2022 service manual, driving it is optional. I haven't had to drive mine that I believe has the same transmission cooler as the tow package (I have the FX4 but no tow). So yes, you are right, it could be at the wrong level if you need to drive it to hit temps.
You can absolutely overfill transmissions (like my old Accord), but you can't overfill this one assuming you're following the procedure of getting the fluid temp to 185-200F and having the leveling plug open.
Those prices are insane. If you don't want to do it yourself or can't, find a local mechanic. There's nothing special about these parts or the fluid changes.
I'm sorry to hear you're having issues with the GM-designed, Ford-built trash that is the 8F35 transmission.
If I were you, here's what I'd do:
1. Find a local mechanic that can toss in a unit from eBay. They're going for $2000 with low mileage shipped to their garage.
2. Sell it right...
7.5k is how long I went on my last one with full synthetic. I had 18% left on my oil minder.
The oil looked quite nasty, but I know that doesn't mean much these days. I'm not comfortable with 10k give my spirited mountain driving/dust/how cheap full synthetic is.
New reports seem to have fallen off a cliff. But interested in input from other folks as well since I think my truck is about to be on its 3rd set in ~30k miles. 😬