I agree the F250 will tow the 29BHS fine, but if I'm not mistaken the Ford OEM receiver has a maximum weight carrying (no WDH) capacity of around 500lbs, and the dry tongue weight of an '07' 29BHS is 765lbs, so I would expect it to actually be a little heavier.
I would borrow a 800lb or 1,000lb rated WDH for the 100 mile trip to be on the safe side. As far as no brake controller, well, the TV brakes will handle the F250 weight just fine, but the additional rolling 5,800lbs "plus" TT behind it could be an issue.
If this were my situation, I would ask a friend that has a TV with a WDH and brake controller to tow the TT the 100 miles....., that's just me.
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