Does your coachman have separate circuits/bulbs for the brake lights and the turn signals? If not, you don't need a converter. Even if you do need a converter, I doubt that it will help with the fuse-blowing problem unless you do a re-wiring job at the same time.
It's fairly easy to do a front-to-back rewire by running a cable along the frame and attaching it with cable ties. Don't assume that the lights in the front are not part of the problem.
If you do rewire, you can install extra in-line fuses in the run to the rear. If the fuses that now blow continue to do so, put a slightly larger fuse in there and a slightly smaller one in the run to the rear. If the rear fuses blow, you know that the problem is in the rear.
2008 Itasca Meridian 37H & 2015 Flagstaff T12RBST
2011 & 2012 Len & Pat's "One lap of America"
27K miles & 41 states in 13 months - Woo Woo
Yellowstone Lake 6-1-2012