When I bought my 4400 lb camper, I went to pick it up with my SRW flatbed.
The flatbed was 7-6 long, but truck was short bed and the camper overloaded my tires by 15 percent, even I anticipated that and moved spare wheel to front bumper.
I made it home OK, but bought dually right after.
So yes, COG is very important if you want to use camper with SRW.
Builders don't pay much attention to COG. On my camper all heavy stuff like batteries, generator, propane tanks are in the rear of the camper.
Holding tanks are under rear bumper, 6 -7 feet behind rear axle.
Only fresh water tank is on front.
Before I bought dually I played with COG. Removed the generator, removed one of the propane tanks, moved the batteries on front of of the flatbed, on side of the camper.
That can make about 200 lb difference on rear axle, but unless you mount front platform and put heavy stuff on it, there is not that much you can do.
Again, moving spare wheel on front bumper makes the biggest difference.