Disclaimer in that we don't have a Ford Transit based class b, we have a Chevy Roadtrek, that is also rear drive, and have dealt with other rear drive stuff.
Offhand, my first impression is not to agree with either of the theories you have been given. While increasing springrate (stiffness) of the rear springs will reduce sway some, it will also harshen the ride, that is the tradeoff in doing it. To reduce sway and wind push, big sway bars are generally more effective and have less detrimental effect the ride harshness.
I don't know what the Transit has in it for sway bars, but it is fairly common in commercial type vans to either have no, or a very small, rear swaybar. This is primarily for safety in empty vans, to prevent oversteer (swapping ends so to speak, when you don't want to). In a fully loaded class b, you can never have the light rear weight of an empty van, so is not an issue, and big sway bars have proven to work well in the Chevies, Dodges, and E series Fords. If you don't need more rideheight also, it is possible that just adding a sway bar in the rear could help your issue a lot.
In our Chevy, we put in airbags to get more road clearance, not stiffer ride (they are actually lower spring rate than the stock leaf springs) and a big rear swaybar. We have since removed the overload leaf from the stock spring packs to soften them and put more of the ride on the softer airbags. We didn't really notice any difference in wind push or sway, as the swaybar takes care of it, and we ride noticeably smoother.
The one thing that some folks will notice, but most won't, is that a big swaybar will harshen big bumps that happen to only one of the wheels, as they are basically just a spring between the two wheels that only does anything when one wheel moves up or down without the other, as in sway. You get the same affect on a single wheel bump, and sometimes it might be noticeable to you. It will still be less than you would get with a stiffer spring in the same conditions, though.