Where can I rent a pickup that allows more than 10000# trailer towing?

Without going into all the details, I need to rent a 3/4 or 1 ton PU from a company that allows towing a trailer in excess of 10000 pounds. It looks like all the rental companies put a maximum for towing at 10K. I need to pick up a machine roughly 500 miles away using a 14 to 16 foot drop deck trailer. The machine weighs roughly 8K and a trailer is likely to be 4 to 5K roughly in that size.

I am limited to the drop deck trailer due to loading and unloading constraints at the pickup end...

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