<aside> Thanks, RobA! I shall try to dispense valid advice, and steer streamdiggers rightly :-) </aside>
Yeah, that helps the river situation some, rentauri. I can sympathize - it's just plain hard to depict a gradual slope! Really, though, a realistic river network does a good job of showing what's higher and what's lower, all by itself. Like RobA said, if geography won't support a particular feature, you can label it magic and just drive on. There's a principle in fantastic fiction, though, of being stingy with extranormal items. One's universe is more engaging if the departures from our own are limited. Present, just limited. For instance, if you want a bunch of harsh history, some of those watercourses could be canals, dug by generations of prisoners slaving away in the blazing sun and driving rain. Or the product of useful earth-benders (my kids have been rerunning Avatar / Last Airbender episodes).
That said, no matter what the reason for some remaining over-connectedness, you could indicate direction of flow by some placement of tributaries. Rivers don't start big, they build up from many smaller streams. Visual direction-of-flow hints come at the junctions - the join is usually at least a little less than 90 degrees, with the resulting angle "pointing" downstream. If you place some tributaries, you'll start to see where the water comes from, and realize that unless there's one heck of a spring at (say) Strohigm or Freetom, it would be hard for multiple major rivers to spread out from one point. More likely, all those mountains have creeks and streams starting, joining, and eventually merging to make the big rivers.
Do you have an app that will help you place text along a curve? Instead of 'claiming the territory' with great big labels, a more conventional approach would be to spread a territorial label out curving across its extent, maybe using a different font or all caps to distinguish from other features' labels. It doesn't even take a terribly large font - such a label will often have letters spaced 'unnaturally far apart' -- look at some old maps and see what looks best to you. Google "16th century map" or the like, and have a nice wander through the University of Texas' online map collection, or any of a dozen others. Search 'map collection' or the like on the Guild - there's been numerous threads with links to stellar examples.
Maybe the islands seem too blobby because they are so rounded. Try putting some sharp points and clefts in places, and see if that helps. If you erase to get channels, you run the risk of your smallest curve being the radius of the eraser brush you use - that looks unnatural. Try some of such erasing really zoomed in, and/or freehand youself a jaggy selection in place and erase all within that.