OP,
IMO, your good to go w/ the 5er your looking at. We towed a similar 5er w/ a '03 F250 SD, CC,4x4,sb, 6.Uh-Oh w/o a problem. Then bought a '15 F350 as the '03 was starting to go south. Awesome truck towing the same 5er. Kids left, ended up getting a new 5er (bigger !!!!) and the '15 did a very good job, but I was over weight limits of truck. Last year went w/ a dually. Also, when we had the '15 and got the new coach in '17, upgraded hitch to a B&W Patriot and it's a OMG "why didn't I do this sooner" hitch !!!!
As for your 7.3, tho am not too familiar w/ it, my guess is that your probly at the upper ends of it limits Others will chime in w/ better knowledge.