Also, I have since found that my iPad 2 has become "like new out of the box" fast performance-wise by doing a variation on a normal erase-reset/restore procedure.
On both my iPad 2 and iPad 3, I did a backup to iTunes, then did and erase-reset restore as new iPad, first. Then, reconnected my iPads to iTunes on my Macs and then, I did a restore from backups.
The performance increase from this were noticeable and apreciable and both iPads are operating with a like new performance speed and, in addition, both iPad models have gotten an appreciable amount of free storage space returned to them.
Here is the procedure for this restore procedure and this has already worked, sucessfully, for one other iPad 2 user so far!
First, connect your iPad to USB and sync and backup your iPad to iTunes (make sure your iTunes is up to date).
Then disconnect/eject your iPad from the computer.
From just the iPad, in the Settings App under the General setting, look in the right column for Reset option, then erase and reset your iPad to completely erase your iPad and then, again, from the iPad, set it up as a new iPad setup to factory "out of the box" operation.
Then reconnect your iPad to the computer and make sure to cancel the syncing, by tapping the small X to the left in the top center iTunes display box.
iTunes should detect your iPad and ask if you want to update to the latest iOS version.
Select OK. If iTunes begins to try and sync, again, cancel the sync. Let the update continue until it loads into the iPad.
May take anywhere from 30 minutes to an hour to update the iPad.
DO NOT WALK AWAY FROM THE COMPUTER DURING THE UPGRADING PROCESS!!!!
Once your iPad is updated and your iPad appears in iTunes, again, CANCEL the sync, once more.
Select Restore from Backup instead and pick your last backup to restore back to your iPad.
Once the restore is complete, finish setting up the iPad and let it sync back to iTunes you can either cancel the sync, again or let it backup, again.
Then disconnect the iPad.
Do one hard reset of your iPad by holding down both the Home and sleep/wake buttons simultaneously until your iPad goes to black and restarts with Apple logo, then release the buttons.
Once your iPad is back to the Home screen,
In the Settings App under the General tab, to the right under Spotlight sesrch, try disabling the search under apps that really do not need a search, like some games, remotes, apps that really do not need to be searched, etc., to reduce the list for Spotlight to search.
Try turning on Reduced Motion.
This is found in the Settings App in the General tab the left panel.
In the right panel look under Accessibility, the look for Reduce Motion and turn this feature "On".
You should see an appreciable performance increase on all iPad 2, 3 and 4 models.
In the Settings App under the General Tab, in the right column, look for Background App Refresh and turn this setting to "off".
If you purchased any music from iTunes, you will need to redownload that content back to your iPad for playing directly from your iPad and not from Apple Music servers.
Also, if your iPad contained a lot of images in the Photos app, these will take time to regenerate the original AND thumbnail images themselves inside of the Photos app when you first launch it.
I update ALL my iDevices connected up to my iMac and sync'd over USB through iTunes.
My Mom"s and Wife's iPad 2s were still both on iOS 7 and my own iPad 3 this way.
I have NEVER, EVER had an issue with any iOS updates.
Glad you got your iPad 2 to a much better performance level than what you experienced previously!
If you choose to try this, your iPad 2 should be even better running!
Good Luck!
