My thoughts on rivers is to do them EXACTLY like Paths that you already have, except with more graphical elements (the river, the riverbank).
Because of how nicely the tiles sit over one another, I genuinely don't think it would look out of place to have a River tile sitting on top of a, e.g. Forest tile.
But also I'm a graphical moron, so maybe it actually would look terrible! That's my two cents though, if it's worth anything :D