I have a similar truck/pin weight to OP. I added Timbrens to reduce the sag from 2 3/4" to 1 1/4" and it helped keep the front loaded. Also I have discovered that there are differences in instructions for hitch rail positioning between rail manufacturers. For instance Reese rails install puts center line about 2 1/2" ahead of axle but Husky Rails install put the center line only 1" ahead of axle. In my case I have Reese rails with a Husky hitch positioned full forward toward cab. This places King Pin about 4" ahead of axle. I suspect that the King Pin on an F250 needs to be between 2-4" ahead of the axle to keep the front axle from unloading. I still don't like being so close on the rear GAWR but I am banking on the fact it has the camper package and is identical to an F350 with higher ratings.
Here are my CAT weights:
F250 6.7L PSD 4X4 Lariat - Full tank, Husky 16k W hitch, me:
Steer Axle - 4720
Drive Axle - 3300
Total - 8020
With 2007 Keystone Challenger 29RKP under tow:
Steer Axle - 4740
Drive Axle - 5980 (vehicle total=10720)
Trailer Axles - 7780
Total - 18500
Trailer:
Pin Weight - 2680
Axle Weight - 7780
Total - 10460
About 700 over published tow vehicle GVWR (10000) but...
1320 under tow vehicle axle ratings (FGAWR=5940 + RGAWR=6100 = 12040)and...
5000 under tow vehicle GCWR.