Not sure if their are any hybrids rated to 7000 lbs or there about. My older sister had the larger Toyota SUV that is a hybrid. Rated at 5000 lbs. She had a single axle Cub Cadet from the 50's. That one did better than the smaller RAV? hybrid with the same trailer.
She had no complaints, but in reality, did not have a lot of towing experience. I wish she would have put brakes on the trailer. She was legal per towing laws, but reality, the weight was a bit much non braked......
You could probably do one of the smaller double axle rigs, or a single axle to around 4000 lbs total and be fine. Reality, the way toyota rates these, it up to 5000 lbs as long as you keep the gvw of the SUV within ratings also.
Marty
92 Navistar dump truck, 7.3L 7 sp, 4.33 gears with a Detroit no spin
2014 Chevy 1500 Dual cab 4x4
92 Red-e-haul 12K equipment trailer