Ya Know,
My list of procedures and modified backup/restore HAS, so far, worked for, now, over a dozen older iPad 2 and 3 users to date.
Everyone's iPad is different in the types of apps that may have got installed that may have affected the operations of some older iPads.
I have no control over what users have installed on their devices AND, IF they have jailbroke their iPads in the past (which can cause all sorts of issues that are beyond what I can help with).
I made no claims of success for every user that tries these, but continue to post my procedures as these HAVE worked for me AND others and it is ALWAYS my hope and intentions ithese will work for everyone, but there have been cases that it has not.
I have NEVER had any issues with ANY iOS upgrades on my older iPads as I have always avoided doing them using the over the air WiFi method AND always chose the more reliable method of upgrading my devices connected to my computer using iTunes to do the upgrades/updates.
You appear to be one of the, unattentionally, unlucky ones.
At any point in time, did you ever upgrade your iPad's iOS using WiFi? If, so, I strongly believe that iOS upgrades have been affccted by Wifi datat download errors that can happen and can't be fixed once the damaged iOS is installed. The only fix for this is to wait for the next upgrade/update and dothe upgrade via iTunes on a computer to see if that will "fix" things.
NONE of this worked for you, at all?
Even the modified backup/restore?
You have seen NO improvement, whatsoever.
Nothing.
The modification to this procedures is once the backup is complete,to disconnect the iPad from the computer and completely set the iPad up as a new, from the iPad, itself, giving your iPad a "clean slate", as it were. Then, set it up as new in iTunes using the latest iTunes 12.3.2.
You got NO improvement there, either?
DId you try another hard reset after you did the restore?
All I can say is I am sorry none of this has worked for you.
It is not my fault.
If you followed everything exactly as I spelled out and you iPad is still running like garbage, I do not know what to add.
Have you tried just running your iPad without WiFi or Bluetooth on just to make sure your iPad isn't being affected by your internet connection. and speed?
One other thing I have added to my list recently as some users have reported to me that turning off Find My Phone/iPad, something I wouldn't really recommend, in Settings App under iCloud has improved their iPad performance. I don't know why this would be unles it's a bug that has only affected some iPads. It has not affected mine.