Denoel, It does seem like having one bike on one side would really make the 347tht unbalanced. With that said though, we have pulled ours about 20K, including to Alaska and back. I switched to LT tires - Firestone HTs. We also have a TST Tire pressure monitoring system and do not notice a significant difference in temps and pressures from one side to the other. Usually the sun shining on one side or the other has the biggest effect. I'm curious what kind of tires you had on when they blew?
Also, we've been through the scales a couple times and I was actually surprised that the weights from side to side are pretty close. Maybe it's the way we load the trailer with other things, but being a full timer I suppose you have that part of it down pretty well.
I load my Road King right in the middle of the D rings and right over the top of one of the aluminum floor joists. I make sure the rear tire is riding over it too. I used a board at first, but did not during our Alaska trip. The floor is as flat as it was when new. If anything was going to dent it, it would have been the roads we traveled to, in, and from AK.
You're right about the engineering too though. The 347tht is a compromise between a toy hauler and a full size 5er, without much beef added in the rear for the toys.