I'm in the same boat with an iPhone 7 Plus 128Gb in the UK having carried out every conceivable permutation of reinstall and update to iOS 11.0.0 and 11.0.1 with backups from various iTunes saves as well as iCloud from a complete wipe.
For comparative purposes, mine takes 4.5 minutes to boot up from off and then begins to freeze after two swipes after unlocking. It also has no haptics, vibrate, sound or Siri. I can also neither make nor receive calls.
I've probably spent 8 hours on the phone with a very knowledgeable Apple Customer Service rep and sent two lots of logs via my iMac but all to no avail after almost a week. She said downgrading to iOS wasn't supported by Apple so it sounds as if there's conflicting advice being given about this.
Reading around the forums, the issue isn't restricted to iPhone 7's but there does seem to be a correlation with some, but not all, third party screen replacements. In some case exactly the same issues have been reported with phones that have never been damaged (see above).
One other factor that has been mentioned in a number of cases is how hot the phone got during the reinstall/upgrade. Mine was still bearable to handle but got very warm front and back and wonder whether the update caused a component failure due to heat? However, this seems unlikely if rolling back to iOS10 removes the fault.
Clearly there's an issue affecting a small percentage of users in a variety of countries but there seems to be no common connection, other than the screen issue but only in some cases.
If I don't get a resolution in the next 24 hours I'm going to drive to my nearest Apple Store and try for an over the counter warranty replacement.
Has anyone else anything new to add/suggest?
(29 September 14.30 BST)