You are correct in your assessment. But I would hit the scales to get an actual measurement once loaded up to verify.
The way I would attack the "problem" is move as much "stuff" to the rear as possible, even if it means sitting things on the bathroom floor, under the kitchen table etc.... And if I am right the black and/or gray is behind the axle? if so use that to balance the rest.
You can also fill the tank as little as possible for shower/hand washing and use water jugs that you transport in the bed of the truck for drinking and dish washing. Or put the water in the bed and transfer to the holding tank once you arrive.
If the truck GVWR is an issue put the water jugs in the bathroom.
IS the spare under the bed? move that to the bumper
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