Rectangular maps! At last, I have them. Alas, I must also do a lot of parameter tweaking. One of the peculiarities I'm running into is large numbers of enclosed basins. Initial land masses are formed using fractional Brownian motion (fBm) algorithm that uses OpenSimplex noise as its basis function. Aside from resulting in some enclosed basins (low points) in the land masses to start with, it also results in a number of islands and peninsulas that can result in basins when portions of land masses collide and there isn't enough subduction for the basin to be closed.
This is not totally unrealistic. There are a number of inland seas and massive lakes on Earth. The Caspian and Aral Seas are good examples of the former, and the Great Lakes of the latter. However, they do seem more prevalent in these maps. Perhaps reducing the number of "octaves" for the fBm will reduce that. I'm not sure yet. It will require some experimentation.
So, to summarize, more progress, but not quite done.