This is super fun! Just played a few and my best on the 5×5 was 0:42. Thanks for sharing!
Love your description too—would love to see a more in-depth write up if you get the time! It's so fun when you can flip from solving something to generating it. I'm also a fan of solving games with code and have made an Upwords bot that plays perfectly but realized I could use it to try to find better "hyperparameters" for the game (like how many points certain bonuses are) by getting it to play itself and having some metric of what a better game would be. Though as you can probably tell from the lack of a link I have yet to do that part.