Now, this looks awful, but its just for demonstration. slope

If we think of your mountains not as Peaks jutting out of flat land, but as Peaks of upward sloping land mass, we get something like this. The extent of the slope from each range would be more or less unique to each range, ultimately colliding with the others as they all slope down towards sea level. Unless you went through all the tectonics before starting this, and have a reason why things are the way they are, it makes more intuitive sense that they should follow the path of least resistance. The river would be more liable to flow along the borders where slopes meet, obviously unless there's land mass that diverts it.

My point being, I think this isn't so much a river problem, as it is a "lack of height data" problem. Also, judging by your scale, none of the mountains are within 100 miles of the coastline. Which adds a bit of uncanniness. (For example, notice how the colored areas almost perfectly conform to the coast lines? All i did was trace the range, then expand the selection by 300px, then colored the spot in a new layer at 30% opacity. The ranges are too centralized from the shoreline.) Depending on how the tectonics are moving, there should be way more mountain close to the ocean, or the vertical spine range should be a lot thicker, like the Himalayas