I wouldn't worry about what it weighs now, I would worry about what it will ever weigh and the GVWR is what you're looking at to estimate that. Sometimes you'll carry more if you fill the tanks and you'll want the tires, wheels and whatever the weight to the dump station. Sometimes the dump station might be a ways away and you'll need to carry this heavier weight until you get to a place to dump the tanks.
Do you have 6,000lb axles (3,000lbs per wheel) or 7,000lbs axles, (3,500lbs per axle)? I would get a tire that surpasses the potential wheel weight and maybe some margin. If you get the 3,040lb tires, that doesn't leave any margin. How much margin you want (if any) will be your call, but I'd definitely get tires that would meet the gross weight maximums at each tire.
If this means you get a different size tires to accomplish this you'll probably have some fit and dimension questions, too. Fortunately, this is not an unusual problem and others have been successful.
There will be plenty of great suggestions coming soon.
Sounds like the '08 F350 has a better GAWR than an '06 (7,000) with a 3.73 differential. Is this what you have or do you have a higher number for the diff. This could increase the capacity if all else is equal. I'm just curious. BTW what is the 5th wheel tow rating and GVWR for your '08 F-350? Again, just comparing with what I know about '06, thanks.
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