The problem with putting a short bed camper on a long bed truck is that you might be shifting the camper's center of gravity back too far. The camper's center of gravity MUST be forward of - or at worst, directly above - the truck's rear axle.
If it falls BEHIND the rear axle, the rear axle acts like the center of one of those playground teeter-totters and actually takes weight OFF the front axle, which can cause steering and handling safety issues.
I agree that physics dictate that COG behind the rear axle is not ideal, however, a short bed compared to a similar make/ model long bed will have no affect on COG- e.g, Dodge trucks. That is, a SB camper on a LB truck has the same distance from rear axle to rear bumper is the same, ergo, no extra COG behind the rear able.
The first image below is my camper as I presently use it- it is a SB camper on a LB truck bed. The second would be the same camper on a SB truck. In both cases, the COG relative to rear axle to rear bumper is the same.


I do strongly agree that tires in the OPs situation is very much a significant weak link.