Here's an updated version not using the plugin. The glitch still happened over the stone platform. Couldn't get it to happen over the grass floor, but wouldn't be surprised if it still did it there too.
I'm starting to think it might have to do with positioning. My platforms are still pretty messily-laid out. But even over completely solid parts, this sometimes happens. Lemme know if anything obvious pops up, otherwise I still appreciate the help.