Contents of 'offline' Mailboxes disappeared after full restore from Time Machine backup

I'm in desperate straights after not being able to see the emails (contents) from 2 x offline mailboxes following a full restore (command + R) from Time Machine. I've been in contact with Apple Support twice and they're scratching their heads and unable to come up with a solution.

I have a mid 2012 MacBook Pro 13 inch running El Capitan 10.11.6 and recently replaced the hard drive with a Crucial MX500 SSD and installed 8GB RAM.

Before replacing the hard drive I made: 1 x Time Machine backup and 1 x entire clone of the original hard drive. Each onto a separate external Lacie hard drive.

I then restored the new SSD drive from the Time Machine backup drive and all seemed relatively OK (bar losing license agreements with Microsoft Office). But my main worry was whether I'd get a smooth Mail restore. And I didn't. This is a HUGE worry to me. Any help would be MASSIVELY appreciated!

In Mail, before I changed the hard drive I had 5 x mailboxes (gmail, hotmail, icloud and 2 x 'offline' mailboxes from previous employers that were not linked to servers). In Mail Preferences I had unticked 'Enable this account' for the 2 x offline mailboxes as I didn't need the constant password reminders for accounts that were now offline and simply acting as archive emails for my reference.

I'd understood emails in these 2 x 'offline' accounts were stored locally on my computer because I could read them when not connected to any network/internet. I also knew Mail stores emails locally.

BUT after restoring from Time Machine onto my new SSD hard drive, Mail, as predicted, downloaded emails for the 3 x accounts linked to servers (gmail, hotmail, icloud) but showed '(0 messages)' for the 2 x offline accounts. I COULD however see the email folder structures for the 2 x offline accounts but each inbox and folder showed (0 messages)!

Mac Support suggested that the emails of the 2 x offline mailboxes might not have been included in a Time Machine backup as I had not 'enabled' the accounts when I made the Time Machine backup from the original hard drive. But surely these emails would be on the clone I made of the original hard drive??!!

Mac Support went on to say that even if I reconnected my original hard drive back into the computer, I might not be export the emails from the offline mailboxes.

I'm at my wits end because the contents of these 2 x offline mailboxes are extremely important. I'd happily consider 3rd party email archiving of the 2 x offline accounts - as long as I can retain access to their contents. In an ideal world I'd like access to them via Mail.

Is there anyone that can help?!1