Separately, the first time I installed the iOS 9 PB and restored from an 8.4 backup, I ended up with lots of bugs.
When I upgraded to the PB without restoring my 8.4 backup, it has been crazy smooth.
The great thing is that there are two methods to doing the same task. You have your way, but I personally prefer DFU/recovery as it's a somewhat more automated process, compared to what you described.
Separately, the first time I installed the iOS 9 PB and restored from an 8.4 backup, I ended up with lots of bugs.
When I upgraded to the PB without restoring my 8.4 backup, it has been crazy smooth.
I had some issues just upgrading from 8.4 to 9 PB1, but instead of restoring without a backup I ended up resetting all settings and that seems to have done the trick (aside from some essentially known existing 9 PB1 issues).
I went ahead and rolled back to 8.4. I did a DFU Restore. I had the 9.0 Public Beta since it came out on my iPhone 5s and it worked ok and I like the new features, but I decided it wasn't stable enough for me yet and I kept getting prompted in the App Store for my login and password. Plus some apps crashed, the camera app glitched at times. The usual stuff you encounter while using a beta. I might wait for the next beta or just wait for the final release.