YouTube should, SHOULD, still have a snap of the video. Most companies, if not all, that run a data centre of any sort, will have a temporary (or even permanent) archive of any pictures, posts, videos or whatever it is you uploaded, especially for social media. This is because they need to have a backup in case something happens to their servers. YouTube may actually genuinely delete videos once you delete it from your channel, but I highly think it's unlikely that the video is permanently deleted right away and would require one to a few days; to be permanently removed from their servers & their backups.
But hopefully re-uploading it will help them. Maybe you could even upload the raw, un-edited footage for extra proof?