Just make sure to remove the beta profile before reverting back. Or else you'll have an update badge but no update until that beta goes into official release.
Ok so I tried your method (mostly).
1.I first made a backup with the 9.3(just in case)
2. downloaded the ipsw for my iPhone 6 iOS 9.2.1 and held option while clicking update in iTunes. Here I selected the ipsw and let iTunes go to work.
3. When the phone powered on it had my photos still, call logs, and messages and the same amount of used data but it was missing almost all of my apps.
4. I proceeded anyway and backed up the old phone to iTunes as 9.2.1.
5. Restored the backup to my new 6s
6. Went to App Store and redownloaded my apps manually
7. All apps went back to their folders automatically. Most of my settings stuck
So this method did the trick but it wasn't very seemless (maybe I screwed something else up)
Also I rushed and forgot to remove the beta profile so my new 6s keeps prompting me to update :/
Thanks lagwagon for the tip. I'm glad I got to restore everything without too much trouble.