I bought the hitch and wiring kit on Quadratec for $89 shipped. It installed perfectly on the stock rear bumper of my 2009 Wrangler X. I can only tow 2000# it says, but I only use the Jeep to tow my 22 ft boat of 4000 lbs for only 3 miles to place in the water and out twice a year. I do have trailer brakes though, still I would never tow on the highway.
Why your hitch won't fit is a mystery, but but obviously it does not do you any good.
I would go back to basics. Although the bumper may be compatible with the Jeep, and the hitch compatible with the stock bumper, that does not mean both hitch and bumper will be compatible with each other.
I like simplicity and find simplicity almost always works. Good luck.
2009 JK Wrangler X, Hard & Soft Tops, Detonator Yellow
Pioneer BT-3300, Polk Audio DB Speakers, Ipod Cable
Mopar Grab Handles, Mopar Slush Mats, Viper 5902,
Wet Okoles, KC Hi-Lites Aux lamps, Cargo Mat,
Safari Doors, Bestop Duster, Windjammer, and Bikini Top.