OP says wrote:
I guess the real question is, if the GCWR is below the 23,500lbs weight rating, but because of the pin weight, is above the 10,000lbs GVWR but below the 6,000lbs GAWR, am I actually considered overweight when it comes to STOPPING the vehicle?
Whew... lots of numbers and questions about numbers
Some points here.
The trucks brakes are a function of the FAWR/RAWR. Your F250 may have a 5000 FAWR and a 6100 RAWR = 11000 lb of braking performance.
Your 375FLF Montana has tandam 7k axles = 14000 lbs of braking performance.
Combined you have 25000 lb of braking performance. Thats assuming all brakes are working properly.
I wouldn't be concerned with braking performance from your '12 F250. Looking at Fleet Fords Body spec sheets shows your F250 have the same front/rear brakes as the F350 SRW.
Ford has over a dozen different GVWR's for the '12 F250/F350 SRW trucks so it makes cents/sense to produce brakes for the highest rating of front and rear axle numbers and apply it to those lines.
I didn't read a "am I overweight" in all those numbers. Legally GVWR doesn't determine how much load the truck can carry. Some owners have reported going over the trucks RAWR/tire load rating by using the newer high GVWR numbers to figure loads.
And GCWR isn't on the vehicles certification placards and also isn't used in any legal sense.
Stay under those GAWRs/tire load rating and you will safely stop and go with your rig.