According to the winnebago website, your trailer has 3500 pound axles, and a GVWR of 7000 pounds.
An example of tires that might be considered would be Hankhook RA08, in 185R-14. This tire is a higher profile ( 82 series ) "commercial" tire that has approximately the same rolling diameter as your existing 205/75-14 tire. The load rating on the Hankook is 1874 ( 3748 for the pair ), which exceeds the axle rating by 248 pounds per axle.
Another example of a potential tire is Kumho 857 in 205R-14. Again, a 82 series tire, so in a 205-14 it is slightly larger in diameter than your standard tire. It's load rating is 2271 ( 4542 for the pair ).
Both of these tires are appropriate for your rim width, have load capacities in excess of the axle capacity, and have higher speed rating than your standard fitment tires.
Both of these are load range D.
Your standard tires are likely load range C, with a load capacity of 1750 or so. You could look on your sidewall to verify that.