Yours has the same gvwr as mine. When I weighed mine at the dump, I only had 700lbs or so of payload capacity with the canopy on the truck. I was wondering if the bigger engine would contribute to a bump in the gvwr but apparently not.
Any of the trucks that came with the 5.4 engine also got the 9.75 rear end, and I believe they tend to have gvwr in the 6800 range (not sure what other factors contribute to the bump up, maybe tow package stuff like tranny cooler, bigger rad). I have poked around on rock auto and the 8.8 and 9.75 seem to use the same brake components, so that wouldn't be it. Perhaps the biggest limiting factors are the size of the rear axle and the load rating of the tires.
Unfortunately, none of this solves the legal limits of the truck, but the real world limits may well be enhanced by a few well thought out adjustments.
My truck had the same sizes tires as yours 235/70 and I bumped up to 235/85 or 31.5" from 28.5". My stock 3.31 gear ratio is now effectively a 3.08-ish. Not so good power and capability wise. For you to go from the same size 28.5" with 3.55 to 285/75 or 33" you are likely at the same 3.08 gear ratio that I am.
Personally, I will be on the lookout for a 9.75 with factory 3.73 gears. With a 2wd, there is only one gear set to think about. If nothing else, you could find a 9.75 with the stock 3.55 (most common ratio out there for these trucks) and at least know you've increased the load carrying abilities (of course, not in a legal sense).
Anyway, digging your build and will update you if I end up upgrading the axle.