This looks from a websearch that I did, that Ford decided to add all sorts of qualifications to the computer programming that evidently controls the relay that sends good power to the charging pin, as you related. I don't think you can conquer this conventionally. I haven't heard of any other brand of truck that has all these computer driven "safeguards" on their towed vehicle battery charging pin. WE SHOULD ALL REMEMBER THAT THE ORIGINAL, PRIMARY PURPOSE, OF THE TOWED VEHICLE CHARGIING PIN IS TO KEEP THE BATTERY IN THE TOWED VEHICLE CONTINUALLY CHARGED UP. SO THAT IF THERE IS A TRAILER DISCONNECT DURING TOWING THE ELECTRIC BRAKES ON THE TRAILER WILL ACTIVATE AND STOP THE RUNAWAY TRAILER!!! Anything (including towing vehicle software) that prevents the trailer battery from being kept at a charge level where it can do its "EMERGENCY JOB", is a highway safety hazard.
What I HAVE read about (I believe on this forum) posted by people who were running inverters, or other higher power devices in their trailers that needed a reliable source of power from the truck's alternator/battery system) was clipping off the factory wiring to the charging pin, wiring their own medium to large current cable in the truck from the battery to the rear of the truck (including appropriate fusing), wiring a separate higher current male/female connector to the umbilical cable and the trailer (thus eliminating the smaller current restrictions of the smaller 7 pin connector charging pin/socket).
I had problems with my Dodge rig for some unknown reason causing the truck 25 amp towing charging fuse to blow intermittently, and me not finding out until the trailer battery had discharged. I installed a 20 amp self resetting circuit breaker inside the umbilical connections box in the pinbox area. If one of my mystery charging system overloads now happens (I haven't had this problem since I made the modification years ago), the self resetting breaker with the lower rating trips BEFORE the truck charging fuse blows, resets when overload is gone, and the truck fuse (with no indicators to tell you it has blown) never blows.