Took me a while to make time to build my circular river, but here it is:
This is the largest area I can enclose with the mix of River tiles that I have.
As a bonus, the 6x6 area inside the river, which uses only tiles from Princess & Dragon plus 3 German Castles, is a torus: the tile edges at the top match the bottom and the tile edges on the left match the right. So, if you remove the river, you can move the topmost row to the bottom, or the rightmost column to the left! (I had to include an odd number of German Castle tiles to compensate for the fact that there are an odd number of city and road edges in the P&D tiles.
This was a lot of fun. I think it makes a quick & fun solitaire game: build a circular river and then draw tiles and place them inside the river. Your score is the number of tiles placed.
Anyway, thanks a lot for posting!