Nick, welcome to Open Roads Forum.
You've obtained an excellent set of scales data.
The minor inconsistency between the 15120# GCW and the 15080# GCW can be resolved by adjusting the 4860# RGAW to 4840# and adjusting the 5580# trailer axle load to 5560#.
That makes both GCWs equal to 15080#.
After the adjustment, the WDH is seen to add 160# to the trailer axles, add 320# to the steer axle, and remove 480# from the drive axle -- a textbook 1:2:3 relationship.
The correct way to estimate tongue weight is to subtract the unhitched TV GVW from the hitched with no WD applied TV GVW.
This gives tongue weight = 9680-8620 = 1060#.
The trailer weight is 15080-8620 = 6460#.
Tongue weight percentage is 1060/6460 = 16.4%. (Not uncommon to see a TH with a TW% greater than 15%.)
NOTE: Tongue weight cannot be calculated using drive axle loads only. You must include the steer axle loads also.
Application of tongue weight caused 440# to be removed from the steer axle.
Loading the WD bars caused 320# to be returned to the steer axle (after making the 20# adjustment in the steer axle load).
The Front Axle Load Restoration (FALR) is 320/440 = 73%.
For your 2013 F-250, Ford says that a FALR of 50% is sufficient.
Since your WDH with existing bars is capable of restoring more steer axle load than Ford specifies, I see no reason to switch to higher-rated bars.
Ron