I have a diesel, but actually that is of little consequence since the weight of the engine is on the front. Your 10K guess is probably light by about 500 pounds, fully loaded. I am carrying about 4900 on the front axle and about 5600 on the rear. My estimates could be off by a few hundred pounds putting me at 6000 at worst. That should still be within my 6400 pound tire load rating.
My concern is not about a few hundred pounds either way but about the meaning of the tire load ratings. So far I have driven my rig over 70k miles. I have had to replace two pairs of tires due to road damage so my existing tires are pretty fresh. I plan to continue to replace the rear tires at about 30k and move them to the front for another 30K at lighter load.