Figured it out. Spotted a comment on a run that clued me into what I was missing. The key bit is holding space on the keyboard, not the controller's drift button, and doing the analog wiggle.

About an hour of clueless wiggling has left me frustrated and having no idea whether I'm doing anything even remotely correctly. The one video that talks about it doesn't really specify the inputs involved, just that it's a wiggle, which is very ambiguous. Can someone actually detail the inputs required to activate it?