A new paper was just posted to the arXiv that develops a polynomial
algorithm for some cases of "2-concentric parallel regular polygons." Here are Figs. 1(a) and 5:

<img src="https://i.sstatic.net/IvD9u.png" width="300" />

<img src="https://i.sstatic.net/y7GTZ.png" width="500" />


> Dhar, Anubhav, Soumita Hait, and Sudeshna Kolay. "Efficient Algorithms for Euclidean Steiner Minimal Tree on Near-Convex Terminal Sets." [arXiv:2307.00254](https://arxiv.org/abs/2307.00254) (2023).

They also obtain results for "$f(n)$-almost convex sets."