Time Machine Backups not in Time Machine

MacBook Air 13" Mid 2011 256gb SSD OS X 10.7.5 - backing up to USB attached 750gb 2.5" HDD

Recently I had some trouble with Outlook and I need to restore my Outlook data from Time Machine. Had trouble doing that until I found that the drive in my MacBook Air (256gb with 150gb free) was just too small to rebuild the Outlook DB. Have cloned my 256gb drive onto a 750gb and this created an issue I don't know how to handle.

Upon plugging the Time Machine backup drive into the MacBook (now running from the cloned drive) Time Machine asked if I would like to 'inherit' the Time Machine backups - this was looking promising. When I entered Time Machine I found that the last 3 months of backups are simply not available. Everything before that is available oddly enough. I can see the backups for the last 3 months if I look into the Time Machine drive in the backups.backupdb folders. See images below for a better understanding.

Prior to the clone and booting from the clone drive I had access to all backups in Time Machine. Is there another way to pull the backups out of the Time Machine drive if Time Machine wont give me access to them?

Can't access them here:

But they are here: