Way to sync CiviCRM memberships to Drupal group
This question gives an answer to a very similar question that you can apply to your situation: Reverse sync CiviCRM groups to Drupal organic groups

However, even with a couple dozen membership types, I still think it might be better to use regular CiviMember-Role sync and use a "limit content access by role" module.  I think Content Access is the popular one.

Try both approaches and see what works for you!