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AFAIK there is no such thing as a shock that gets stiffer the more you bounce it. There's variable valving like the sensa-tracs have, however that is based on compression and rebound speed and length, not frequency.
Please check the label in the door jamb with the VIN. You are looking for GVWR. That is NOT the trailer tow rating, it is the maximum legal weight for vehicle, occupants, and any cargo.
Altering the front ride height on a TTB truck will mess with the alignment. Raising it will cause a positive camber situation, wearing the outside edges of the tires faster. It will also affect the toe (since the two are corresponding). Raising the ride height will not increase payload or towing capabilities.
The shocks with the little coil springs on them are for occasional use tow vehicles like SUVs and minivans. I installed some recently on a Caravan that was upfitted with a wheel chair ramp and dropped floor. They are designed to reduce sagging (and also the headlight aim problem associated with it), not increase towing capacity. The shock mounts are not designed or intended to handle a substantial amount of weight, since shocks do not affect the ride height of a vehicle and they do not carry weight. Springs do those jobs.
So are you trying to say that yours do this??? A shock that is shot will do this!!! it will have no compression or rebound dapening until it pumps oil up into the shock valving. SO YES there is such a thing just needs to be totaly worn out... A shock, really just slows the rebound of the spring, without them it is a...... Well, Spring.
I am glad you have a HD f150. I am not contradicting you but to tow that much more weight with 1/2 ton rated brakes you might want to stay away from any steep decents, you will let all the smoke out of your brakes and get to the bottom of the hill really fast.
I bet a f150 will get to the top of a grade with that load but I bet it will go down hill real fast. I am impressed by your truck's capabilities, that is one other reason that a diesel engine can be more effective in a heavy truck, the auxillary engine braking components available for them unfittable for a gas truck.
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