You should not, IMO, put incorrect or bogus information in tags for the purpose of sorting. It just creates more problems down the road, again, IMO.
What I would do would be to either find an unused tag to re-purpose (like Keyword or Occasion or whatever) or create a custom tag specifically for this, and then tag everything either "Album" or "Single" in that field. Then I'd use that field for my first sort field.
A smile is happiness you'll find right under your nose.