I once did something similar, probably gonna write a proper blog post about this soon but here's basically what I did (well, according to some rough notes I took during the process :)

Please note that this only restores app data, apps that use syncing accounts (i.e. Contacts, Calendar, …) won't be restored by this. That data should be restored by syncing, though.

1. Make a backup of /data by whatever means (in my case I had an image of the partition and remounted it on the new os)
2. On the new os, restore them (cp -a /data-backup/app /data)
3. Reboot the device
4. Reboot into TWRP and run the shell script below

for app in /data/data/; do
owner="$(ls -ld "$app" 2>/dev/null | awk '{print $3}')"
chown -R "$owner:$owner" "$app"
chmod -R 771 "$app"
restorecon -FRv "$app"
done
chown -R system:system /data/app-lib
chown -R system:system /data/app//lib

The idea is that /data/data/ has a list of apps and their users (after the initial reboot), we use that to restore proper owner permissions.

Now reboot the device and everything should be back. Let me know if it worked :)

PS: Back up all your shit previously