As I say, it's worth a try (set Movie to Replay) based on your observations thus far.
It must be said that Mavericks 10.9 is MUCH more aggressive about Power Management for Foreground versus Background applications than any OS before it and I doubt that Control:Mac has taken that into account.
So, if you wish to try, I would set the Movie to Replay... and then set Control:Mac to Backup and leave it as the Foreground application... then leave Display to Sleep... but everything else stays on.
Won't hurt to try.
And if it doesn't work, you've already seen how well FreeFileSync works to copy a Library... so maybe use that as your Backup routine rather than the compromised one within Control:Mac. I certainly gave up using it a long time ago. Cloning plus File Sync much is quicker, more robust with Audit Logs for my needs... but YMMV.