Even in a travel trailer with a straight drop from the toilet into the black tank, toilet paper will occasionally get caught up in the toilet. Through trial and error, I've learned a trick that may help with your situation. Before you sit down, depress the flush lever slightly to fill the toilet about 1/3 full of water - similar to what your S&B toilet has in it all the time. As you fill the bowl with paper, it will absorb the water and compact a little - giving you more room for more paper (without it contacting you bottom). When you're ready to flush, add a little more water, until it covers (or nearly covers) the paper. Then flush. The additional water will help flush the paper out of the toilet without it sticking to the sides of the bowl. If you need to add more paper after your initial flush, add more water first (again, to about 1/3 full) before adding more paper, and again before you flush again.
This procedure may help with your situation, too. Yes, it uses more water, but it sure beats the alternative of having paper clogs stuck on your ledge. In addition, I've found that it helps eliminate (or at least minimizes) "skid marks" in the bowl.