Kickstarter approved my proposal after all. While the original rejection message didn’t seem like there was room for reconsideration, I posted some messages on my proposal page (as well as through their support form) and was able to follow-up with the moderator. The review process certainly felt klunky and was quite frustrating, but at least I eventually got the go-ahead.
I’m working on the video today, and should have the project page up in time for Maker Faire this weekend. Hooray!