Looks like it's a bug, just tried Level 2 in-browser and always died before making it to the switch. My best guess is framerate/connection differences between HTML5 and standalone versions, since we noticed the game ran slower in-browser vs in-engine (or we just used a wrong time variable).
Per the jam rules, I think we'll leave it as is until the voting period is over unless a lot of people run into this issue, but thanks for catching this!