Pathfinding to a moving target in evolving terrain

I recently published a free browser game, developed in Unity, called  Build + Brawl. In Build + Brawl, the player moves their character to avoid swarms of approaching enemies. The environment contains impassable obstacles  —  some generated at random, some placed by the player — that the enemies must route around as they approach the player. There are off-the-shelf solutions for pathfinding in general using algorithms like A* [1]; however, there were a few quirks to Build + Brawl that pushed me to roll my own solution:

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