I tried something a bit like this a couple of Jams ago, but I made it too complicated and nobody played it. Congratulations for making a simple idea so compelling! Not easy to do at all, especially in a few short days.
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yeah it's not easy, and this is worst-case scenario for networking! I wrote a blog post if you're interested :) https://wayfarer-games.com/blog/one-button-mmo/
Just read the blog. I love how seriously you've treated this seemingly trivial game. You've thought it all through, done the hard work and the results speak volumes! My attempts at multiplayer have been rather less robust. Perfectly serviceable for the volumes the received, but wouldn't stand up to a serious amount of traffic.