"tar -xvf backupfile.tar -C /storage/stuff" should unpack things into /storage/stuff overriding the embedded paths. Just untar the backup to a specific subfolder on the (new) SD card and then "systemctl stop kodi" before moving things around as required and "systemctl start kodi" when done.
NB: An older OE install has probably accumulated a fair chunk of cruft over time so I'd be selective and only move Thumbs/DB's and sources.xml over to start. I'd reinstall add-ons new from repo's and only copy configs over if needed.