Well, you are right about those rivers.

My suggestion would be to look at the mountains and try to figure out where the rivers would flow from "lay of the land". As the River Police will tell you, rivers flow from high to low, meaning that they start in the high land and flow out to the plains. Some of yours seem to start at the plains and run up to the mountains and then down again to the sea. There are quite a few that would look good if the "mountain" part were cut so that they started there instead if passing through the mountain.

I do like the way they meander, just make sure that they go around the high ground instead of over them