As a composer I have dealt with this and had contracts written up a few times, mainly as a composer and performer simultaneously---so it's a little different.
I believe you're pretty close on what you need. With that being said, I still use a lawyer when anything is important, so don't take my advice for anything other than a---very non-legal---opinion. When in doubt get a lawyer.
If I'm understanding the situation correctly, I would think that the performer/recorder would own the master (since they own the master recording) and the composer would have the sync (since they are the songwriter, but don't own the recordings). Each person has a key and you need both to open the door.
Here's an article I found that kind of lays it out. I hope this helps.
https://www.thebalancecareers.com/sy...ensing-3971888
I think mlesemann makes a good point with the Bach example. Since the song is now public domain, No sync license would be needed. But the recording is copyrighted, and therefore needs a Master Use license.