Here is a proposed idea which I can't imagine would be too hard to implement. A public game which also allows invites. In other words, in a six person game I could send emails to three friends of mine and let anyone else join the other two seats. 

It could be set up so that you can invite players to a public game... however to make it fair for ranking purposes anyone would be allowed to fill all the slots.

i.e. spaces would not be reserved for the invited players.

This is not dissimilar from tournaments.  I'm pretty sure I can create a public tournament, and also send out individual invitations, right?

Yes exactly.

Why not have public non ranked games?
Either way, if you have public ranked games with invites, I think it should be clear that this was the case when joining the game (i.e. knowing that you are joining an open slot in a six player game where three of the players were directly invited and which players were direct invites).

2nd the public nonranked option

Alpha wrote:

..if you have public ranked games with invites, I think it should be clear that this was the case when joining the game (i.e. knowing that you are joining an open slot in a six player game where three of the players were directly invited and which players were direct invites).

I agree with Alpha on this point.