265'x16 won't support your rear weight ? I thought you looked into that when you bought this new camper . Those OEM GM wheels have a 3500/3700 rating. tires = 6830.
You might need a spare tire too, check into that. If you do, where will you carry it ? Under the truck in the OEM carrier ? Maybe , maybe not depending on the size.
You have limited slips in your 4x4 , so be careful with tire size on the same axle.
Look into swapping one of the fronts to the rear and maybe you could get away with running 2 diff diameters on the front for a short ride if you had to.
As I have found out , a lot of places are closed on Sundays , so finding a new tire to match a 19.5 might take a few days .
The new tires will raise the height of the whole package, you might feel that in crosswinds. I know it's only an inch but it's a 16 ft long inch on a SB truck.
I assume your warranty is expired . GM might not like the idea of a tire swap.
There are a lot of extra expenses that tag along with the 19.5's (mount and bal., off set )
Look at it on the Rickson Wheel website.
The trade value of your truck plus the money $4-5k spent on upgrading it to fit the new camper might be a down pay on a new or different (new to you) truck heavy enough to do what you need w/o mods.