It sounds like you just need to stiffen up the area between the toilet and the tank. If the toilet hole is in the original location a standard RV style toilet should work fine without hanging over the side. I used one similar to this...Toilet
. The black tank is not strong enough by itself to support the weight. So, you will need to insert some plywood between the black tank and the shelf to stiffen the shelf. Cut a hole in that plywood big enough for the opening first, then insert it where it needs to go. Buy a new toilet flange like these...Floor Flanges
Pick a flange that has enough distance below the flange to compensate for the extra thickness of the plywood. Screw the flange down and screw it to the plywood. Now you can place your toilet on the new flange and bolt it down. The whole thing should be sturdy now.