The good news first;
Based on the information you supplied about your F150, and what we know about the 2010 256RKS, I agree with you that your F150 is a nice fit for the 256RKS. IMO up-grading your TV now isn't required unless you plan to upgrade your TT in the near future
The following data may be a little overkill, but may be helpful for those reviewing your thread......,
I thought we would first work with your 2010 256RKS under two different loaded conditions, one at the GVWR of 7,350lbs (Jayco website).
RV and WDH manufactures recommend the loaded TT tongue weight to be 10% to 15% of the loaded TT weight...., however, 13% to 15% will enhance TV handling of your 28ft long TT. Knowing the potential loaded tongue weight one can than confirm that the TV's receiver is rated correctly in the WD mode, and for sizing the correct WDH spring bars.
Under "maximum" TT loaded conditions: 13% to 15% of 7,350lbs = 955lbs to 1,102lbs.
Under a hypothetical loaded condition: 13% to 15% of 6,720lbs = 874lbs to 1,008lbs.
5,570lbs (UVW) + 200lbs (added for actual ship weight) + 150lbs (battery, WDH, etc.) + 800lbs (cargo, stuff) = 6,720lbs Loaded TT weight.
Towing Capacity 9,300lbs
Payload Capacity ?
The 5.4L with the 3.73 gear ratio is a nice drivetrain for towing a TT. As you may know, usually the first weight limit that can be max'd out with many 1/2 tons is the payload capacity. What many folks overlook is the fact that the TT's loaded tongue weight is subtracted from a TV's payload capacity.
15,000lbs (TV GCVWR) - 7,350lbs (TT GVWR) = 7,650lbs for TV.
15,000lbs (TV GCVWR) - 6,720lbs (TT hypothetical) = 8,280lbs for TV
In both cases above the TV weights remaining are higher than the TV's GVWR of 7,200lbs, this is good as long as you don't exceed your F150's GVWR.
The only unknown is your F150's specified payload capacity. The sum total of the TT loaded tongue weight, TV passenger weights, and TV cargo weight must not exceed the specified payload capacity (reference tongue weights above).
Your "actual" tow rating is less than published tow rating of 9,300lbs, to get your actual tow rating you subtract the sum total weights of TV options, TV passengers, and TV cargo. http://www.jaycoowners.com/showthread.php?t=3866
In cases where actual weights aren't known (or to avoid number crunching), some folks will use 80% of the the published tow rating as a "not to exceed" GVWR for a TT choice. Using this ball-parking method 80% of your 9,300lbs = 7,440lbs maximum TT GVWR....., so you are still good.
If you get a chance, for fun hit a CAT scale if the opportunity arises: http://www.jaycoowners.com/showthread.php?t=3871
watch that you don't exceed your TV's GVWR (overloading TV box, etc.) and/or payload capacity (which includes tongue weight). Also confirm that your receiver is up to the task as well (it should be fine).
I apologize for the information overload, I was on a roll this evening