That's not correct.
Your class II hitch is rated for a maximum of 350 lb tongue weight and 3,500 lb total trailer weight regardless of engine or gearing.
You will have to upgrade to a class III hitch to exceed this. Keep in mind that your Explorer has the 3.55 gearing instead of the 3.73 which was included with the tow package. I also believe that the tow package equipped Explorers also had an engine oil cooler. They both use the same stand alone trans cooler.
Just by installing a class III hitch you can safely pull 500 lbs tongue weight and 3,500 total trailer weight. You could technically pull more trailer weight with the class III hitch although I wouldn't subject your vehicle to it without the gearing.