Hate to double-post (not really sure what the policy for that is here, if this is frowned upon I'll just merge this post into my last) but I've managed a major breakthrough in making my map, which I think will speak for itself.
I'm extremely happy with my results, and if there's interest, I'll do up a tutorial to show how I did my landmass features. It's a complicated process, but I completely avoided converting my contour lines into a heightmap and instead heavily beveled and smudged all of my contour layers. I gave each layer about a 30% opacity. I adusted how dark the bevel was depending on what height that particular contour line represented, and of course, I made sure my bevels took my rivers and lakes into account too.
The stairstep pattern on the upper continent looks like it's there to stay, unfortunately. I've heavily worked it already, and anything else I've tried to make the banding look smoother has only made that continent look worse.
Any comments for how I might be able to make this map even better would be highly appreciated!