Alas, I haven't made enough progress today to have something to show. I will briefly mention that in the approach to terrain generation that I'm thinking of, various functions such as sine, cosine, sawtooth, and triangle waves can be combined with linear shapes (such as polylines, splines, etc.) and noise functions to produce terrain.
This is hardly novel, in and of itself. Several articles on the subject have been written over the past decade. Here's a brief list of some of them.
Soon Tee Teoh. River and Coastal Action in Automatic Terrain Generation. Proceedings of the 2008 International Conference on Computer Graphics & Virtual Reality, CGVR 2008, July 14-17, 2008, Las Vegas, Nevada, USA
Houssam Hnaidi et al. Feature based terrain generation using diffusion equation. Pacific Graphics Volume 29 (2010), Number 7
J.D. Génevaux et al. Terrain Modeling from Feature Primitives. Computer Graphics Forum 2015