Someone could (I think) write an extension to prefetch Youtube video links, download with youtube-dl to /tmp, and then re-embed the local file when you visit the page. Could be tuned to waste less space or use AWS for quicker download speed.
That sounds unnecessarily complicated. You should be able to write an extension that simply bypasses the Youtube player (possibly looking at the youtube-dl source to figure out how to find the video file itself).
"Bypass the Youtube player" is what I meant, but reasons to use as is: its interface is simple, it's maintained (this is a hack, why trouble yourself when youtube breaks things), and you won't have to read this: https://github.com/rg3/youtube-dl/blob/master/youtube_dl/ext...