Allow only existing CiviCRM contacts to create own Drupal account
A couple of thoughts.

If you want this to be a response to an action - eg you folk send out a mailing - then you can do this via a webform - send out a link with checksum to a webform and upon submitting the webform you can trigger Drupal Rules (we usually do this by giving them a civicrm Tag) and this can also instantly log them in

If you want to do this as a self-service then I would probably be adding a wee form for folk to say 'send me a login link', they enter their email, it sends them a checksum and then you do the above approach of another webform.