I did reread your post and I see now you didn't say anything about a cooler thermostat.
So apparently you had a faulty thermostat.
Glad you got it figured out.
Mine is not over cooling, 170 thermostat does just what it's suppose to do.
If I don't put a load on the engine it will cool down to 170
I've changed my thermostat at least a dozen and half times, never had to do any kind of procedure to burp the system.
When I'm done swapping out the thermostat,
I leave the radiator cap off until the engine gets up to operating temp and you can tell when that happens if you look down the radiator fill opening, water will flow quite fast and drop down in level.
Just before that happens it will rise a bit, because the antifreeze is starting to expand and entering the radiator through the bottom hose.
I then proceed to fill what ever the system needs, which is close to the amount I siphoned out.
I'll put the cap on and throw the little bit left into the over-flow tank.
I also make sure the over flow tube is not hanging down too low or kinked in anyway.
I actually cut the tube shorter so at no point is the tube lower than the radiator cap.
I've run into that problem on other vehicles, with a big loop in the tube the air has a hard time getting to the over-flow tank.
I should also mention I did buy a new radiator cap two years ago, it started leaking.
I'm pointing that out because if the cap is bad also it will suck in air from the cap and not the antifreeze from over-flow tank, just something to think about.
The Raptors radiator cap is 20 psi.
https://www.tascaparts.com/oem-parts/ford-radiator-cap-6l2z8100ac/?c=Zz1jb29saW5nLXN5c3RlbSZzPXJhZGlhdG9yLWFuZC1jb21wb25lbnRzJmk9TUEwOTA4MTUmcj00JmE9Zm9yZCZvPWYtMTUwJnk9MjAxMCZ0PXN2dC1yYXB0b3ImZT02LTJsLXY4LWdhcw==