Earlier quoted context omitted.
The OP actually cites that project as the method they use for initial polygon generation, and tells everyone to go read it.
If you want to lose a few weeks hacking away at something kind of fun, then turn around and try to implement the Fortune's Algorithm[1] Voronoi region/Delauney Triangulation method that underlies Amit's map generator. Somewhere I have a WinForms app I built a while back that animates the process and draws everything out step by step. [1] https://en.wikipedia.org/wiki/Fortune%27s_algorithm
We didn't use Fortune's for historical reasons (the first versions of the code were in Fortran 77, and written well before he published his paper). Instead we generated triangulations and then flipped edges until they were Delaunay, and then used the corresponding Voronoi diagram. It turns out that flipping edges to produce a nicer triangulation is reasonable in two dimensions, but intractable in 3D and up.