I added the PA deeper pan on my 2010 GT auto ( 5R5SS)..which now uses an extra 4 qts. It also comes with a locking style dipstick, next to battery, on the firewall. Big enough to also add ATF if required. Deeper pan also comes with a drain plug. To change ATF, you really need to drain the tq converter as well. I used RP max ATF synthetic.
One thing I did notice, was when stone cold, the ATF is higher on the dipstick..... and drops a bunch when tranny heats up.
The oem setup to check / change atf is goofy at best.
I'm 99% convinced you are low on ATF.
In my case, I also add a JDM engineering catch can to the 5r55s, so it won't puke atf all over the ground. Without the dipstick, you have no clue how much atf is actually in there. I also added a 2nd auto tranny cooler, in series with the oem tranny cooler... ( made by B+M, 13 K btu).
To get all the atf out, local ford dealer applied air pressure at the 2nd tranny cooler....and a vac on the other leg. Then it all comes out.
Even then, I had to tweak the ATF level...such that level was normal..... but only when up to normal max temp, which is 170 deg F..as indicated on my aeroforce digital gauges plugged into obd port. Stone cold, the level reads way higher than the high line. Before that extra atf added, it was shifting a bit strange, once warmed up. I had to add an extra 1-2 qts. You could also have some air in there some where.