The same team have found a new ein stein, called Spectre:
https://arxiv.org/pdf/2305.17743.pdf
This one tesselates without reflection, though it does have curves.

Indeed yes – I'm working on implementation of that one as we speak. It will appear in Loopy in due course (current status: playable but the code needs polishing), and I'll be writing a sequel post about that one, because its metatile hierarchy is entirely different from the hat (even though the tiles themselves are so similar), so it calls for a rework of all the details of the generation algorithm.

Now implemented in Loopy (without the optional curves), and my own writeup lives at https://www.chiark.greenend.org.uk/~sgtatham/quasiblog/aperiodic-spectre/