The original suggestion was to perhaps consider prioritizing full 7 player games or even ranked games over unranked or shorthanded games on the Home page where Live Games appear.
This did not seem the right way to go, because a player wanting to play an unranked live game or a shorthanded one has just as much right to put one up as players wanting a full game. However there do appear to be some issues with the Live Games handling procedures, because it is possible for people to more or less seize control of the live games queue by opening multiple live games, meaning that there is little opportunity for others to try their own games. The Home live game only stays on the home page for an hour anyway, so if it does not fill then another game can be picked up.
Based on discussion in the Suggestion, we are going to try a more equitable approach to Live games. Basically, if a player has a Live game open (waiting for players or active in its Live period) then that player cannot open any new live games. If the open game is killed or if an active live game moves out of its live period, then the player is now able to open a new one. This seems to be fair and equitable to all. It does mean a player can't play simultaneously in two live games in their own live periods, but frankly I don't see how you can give proper attention to one game playing live if you have another also playing live

We'll see how it works - we can always go back to the old way or try another if we feel that is better, but I feel pretty good that this is the fairest route for all.