What kind of issues did you have syncing with youtube videos and what kind of latency do you experience? BTW Great initiative and certainly could use that tech for many avenues like remote classroom, any presentation with Q&A. Few others I suspect, but great start.
Technically syncing is easy, websocket + Youtube API. The biggest issue for UX though is that a user should click on the video at least once. Otherwise, Firefox will block sync commands. The latency can be 3-5 seconds for the first sync, when the video is initialized and unbuffered. For the next syncs its < 1 second.
With workout videos usually 120-140 BPM, sub second, let's say 1 second for ease on 120 BPM would be 2 beats per second and so a sync of 2 beat offset would be spot on. Now a 140 BPM would be 3 beats, but you get the idea. By syncing the beats with an offset to cater for the latency and the BPM, you can give the illusion of perfect video sync. More so when doing repetitive motion to that beat, just seems like it would work really well. Certainly makes management of latency a much more easier task and allow for buffering as well depending upon how many beats you want to offset, so could handle latency spikes and brief drops. Which again, makes the things easier when you can control and fix latency , though as you can't do that, planning it out of the equation is always a treat. Food for thought perhaps.
But it is your baby, you pick the formula you want to feed it. But hope you do well whatever direction as certainly has potential in many avenues. Remote rave anybody :).