It 2 is currently playable start to finish in the Pico-8 IDE, in a Windows build, and in a web build on Windows Firefox and Windows Chrome. It crashes very early on in Android Firefox, Android Chrome, and in the Xbox Series Edge browser.
I've been using an undocumented feature of Pico-8 called "high memory video mapping" to switch between multiple banks of sprites. I had been warned that this feature might be unstable in a web build, so I'd been testing it -- but only on desktop, until now.
High memory video mapping was inspired by a library by pancelor that did the same thing by copying sprite data into video memory as needed. If I switch to using that library, I'll have to golf 184 tokens, which is nontrivial at this point -- I've already golfed the easy stuff, ~820 tokens worth -- but should be doable.