Towing a 2720SL with a V6 Ford Explorer

Hi everyone. I have a 2006 Ford Explorer V6, 4WD, with a 3.55 axle ratio. It is factory equipped with a class II hitch, transmission cooler and electrical hookup.
Does anyone have any experience or advice about towing a TM 2720SL (2865 pounds unloaded) with this vehicle? (I'm considering buying one)
The hitch is rated at 3000#, the vehicle at 3230#. If I load the TM up, it will exceed specs.
Should I change to a Class III hitch?
Should I use stabilizer bars?
Does the low wind resistance of the TM change the towing specs in any way?
To go way out on a limb, I may be able to swap the rear axle for a 3.73 ratio, which, with a class III hitch, gives me a 5390# payload. Anyone have any experience with this probably stupid idea?
Thanks in advance.
Jeff