The blog post is lacking critical details stating what exactly the problem definition is. But making some assumptions, I believe the objective is to find a decently short path using less computation time than A*, rather than to specifically find the shortest path.

I will direct the author to any number of references in the field of robotic motion planning. These are algorithms designed to deal with continuous spaces, which is the limiting case of the author's problem with too fine grained a resolution in the A* search graph.

Checking the textbook on my shelf, Principles of Robot Motion (2005), I find an algorithm called "Tangent Bug" within the first 30 pages, which is similar in spirit to the author's proposed approach. The textbook goes on for 500 more pages to develop a host of more sophisticated techniques, including "sampling-based planning," which the author may find extremely useful.

Edit: Just recalled this excellent blog post of Casey Muratori on using one of the sampling algorithms, "RRT", for The Witness: https://caseymuratori.com/blog_0005