SRW pickups were never intended to haul heavy truck campers. That's why God made Dooleys.
3,190 max weight capacity for each rear tire means 6,380 max weight capacity on the rear axle. So that means about 11,000 pounds max GVW. Or 1,100 pounds over the max GVWR of 9,900 pounds for your truck. If your wet and loaded truck weighs 7,000 pounds before you load the camper, then you'll be right up against the tire capacity with a 3,200 pound payload. But if you also tie onto a trailer, you'll overload the tires. And if your wet and loaded truck (including passengers) weighs more than 7,000 pounds, or if your wet and loaded camper (no passengers) weighs more than 3,200, you'll overload the tires.
'99-'04 F-350 SRW with 16" tires has a rear axle weight capacity of 6,830 which is more than your tire capacity. So if you ignore the GVWR of the truck, then tire capacity seems to be your next limiter.
Bigfoot tires are indended for show.
LOOK AT ME!. They are not intended to be work tires, hauling max weight. LT265/75R16E tires came on your truck, and that's what you should use to haul that camper. Then the tire capacity of 6,830 pounds on the rear axle will match the axle capacity. You'll still be overloaded over the GVWR of the truck, but not so dangerously close to being overloaded over the tire capacity.
And if you insist on bigger-than-stock-size tires, you can get BFGoodrich AllTerrain LT285/75R16E tires that have 3,750 pounds weight capacity when pumped up to 80 PSI.
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...I should have 10 PLY tires, and from what I have discovered the LT31675R are only 3 PLY
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You're mixing up your apples and your oranges.
Don't confuse "ply rating" with real plies.
Your load range D tires are equivalent to the old 8-ply rating. Load range E tires are equivalent to the old 10-ply rating. But most radial tires have only two actual plies in the sidewall. Your expensive tires have 3 plies in the sidewall, or half again as much as ordinary LT tires. No modern tire is going to have more than three actual plies in the sidewall.
Think of a "ply" as a piece of cloth, similar to bedsheet material. Way back when, tire plies were cotton cloth. But then along came the much-stronger nylon and polyester fabrics, and the tire makers could achieve the same strength with only two plies in the sidewall (plus 4 plies in the belt of a radial tire). Then steel plies were made, as well as fiberglass-reinforced cloth plies. So today my 10-ply-rating tires have 4 steel plies in the belt plus 3 steel plies in the sidewall.
So tire language changed. Instead of a 6-ply tire, you had a 6-ply-rated tire that had less than 6 actual plies. Then several years ago ply ratings were replaced by load range. And right now load range is obsolete, replaced by Service Description, which is made up of Speed Rating and Load Index.
Tire Tech Information - How to Read Speed Rating, Load Index & Service Descriptions
