I would confirm the weight ratings on your F-250's OEM receiver. There should be two rating modes stamped on the receiver: "Weight Carrying" (w/o using a WDH) and "Weight Distribution" (with WDH). Knowing one's "loaded" tongue weight is the only way to confirm which mode will apply.
Also, the main function of a WDH is to return the required weight to the TV's front suspension that was removed do to the effect of the TT's loaded tongue weight being placed on the hitch ball. Basically you want the weight on the TV's from suspension to be the same unhitched/hitched unless your TV's owners manual states otherwise.
IMO taking your TV/TT combination to a CAT scale and weighing it will confirm all your weights and WDH adjustments (and confirm if a WDH is required). When using air bags it's my understanding that prior to hitching/engaging/adjusting a WDH the air bag pressure should be set at factory minimum PSI, after hitching/engaging the WDH then additional air can be added to the air bags as needed.
CAT scale TV/TT 'how-to': http://www.jaycoowners.com/forums/f37/how-to-weigh-your-tv-tt-3871.html
Yes, your correct that a sway control device should be utilized at all times.