A 2500 would not allow you to necessarily tow a ton more....Towing restrictions are based more on engine and gearing than payload of a truck...So unless you increased the engine size...you would probably be nearly in the same boat (a quick glance at the mfg website will tell you this)....true the 2500 would have been perhaps better to put your quad in the box, but towing (with same engine/gearing) will be very similar....
I have a 2005 F150...with the 5.4L and 373's in the rear (rated to tow 9400)....I tow a 29.5' (bumper to pin) hardwall trailer w/slide...I'm going off memory here, I think it weighs roughly 6500 dry.....loaded with water...I have NO issues pulling....
She definitely works a little harder going up a hill or passing...but it goes....not to mention the Fuel Mileage goes

(good thing I have 135L tank)while pulling....but in terms of capability...it does the job...NO PROB..
I don't think you will have any issues at all.....