Wow, this is an amazing game! Feels really good! I played the web build, and didn't experience any noticeable lag. The background music did cut out, though.
Probably this is just because web browsers have pretty limited memory, your music files are like 22 MB each, and you're loading them all at once. Chip tunes can generally withstand much lower bit depth than most music, so you might try using a tool like Audacity to reduce those monsters down to a more reasonable size. This will also make them load much faster (especially in the web browser, since those files have to be transferred to the client before they can play).
You should point out in your controls that you can use WASD or arrow keys (or, I bet, a gamepad, since you basically get that for free in Mini Micro — though you'd have to explicitly check for a jump button). For me it was more comfortable to play with arrow keys + spacebar.
I really love the idea of playing the same game through several generations of hardware! I definitely want to try again once the jumping-off-ladders issue is fixed. Great work!