OP says wrote:
After being left holding the bag by Furd, when I got my Chevy I made a trip to the scales again, loaded to the max, and worked up this chart.
Scale Ticket Information
Empty Loaded
Steer Axle 4200 4620
Drive Axle 3140 5560
Truck Weight 7340 10180
Trailer Axles (Combined) 8040
Gross Combined Weight (GCW) 18220
Looking at Fords Fleet specs IMO your F250 has a 5250 FAWR and a 6100 RAWR. Your loaded and hooked up axle weights are well under the max. Looks like a good match there.
Your pin weight is the difference in the the trucks loaded rear axle (5560 lbs) and the truck unloaded rear axle (3140 lbs) = 2420 lb pin weight.
Looks like a well matched combo.