I know it's prob not very close to the same weight, but I use a 2006 Polaris Hawkeye 300 2x4 to pull my jetski & trailer around just fine. My father inlaw uses a Honda 250 4wheeler to pull his 14ft trailer around. Although I wouldn't really say go out and buy a 4wheeler for just that. Maybe a bit more aggressive tire on the lawnmower and add a counter weight to the front. If you could weld a removable basket on the front of the mower, or even a spike and put some old workout weights or cinder blocks on/in that would help keep the front down. Maybe park the camper tires on some pavers and then a few in front like a short path just to help it start rolling easier.