To start, anything you do will not make everyone happy. The trick is to get the majority to be happy. I have tried a couple different ways and I currently run two different systems.
For bigger games I run the list all the way through the table until they make it to the main table. Example 3 games - 3 feeds 2, 2 feeds 1 (main game). The players that are playing in the bigger games are there to play, so the movement taking place between tables is at a slower pace.
Smaller games you have more players looking for entertainment and don't have the scratch to play for very long. Seats are opening constantly. When I ran the must move as listed above I had more upset players becasue they were always on the move. At times lucky to play one round before getting moved again.
So for smaller games I have only on feeder table (the last table open). If I had 4 $1-2 NL games, table 4 would feed table 3, 2, & 1 (all 3 main tables). Once a player has been moved out of the feeder game they will not be required to move. For players that still would like to get to the first game or any other game I will run a table change list.
For both situations I run what I call the 8 man rule. If the feeder table is below 8 players and the main game has 8 or more players and do not move a player until the feeder table reaches 8 players. I will continue to move players anytime the feeder table has 8 or more players until main games are full. If a main game falls below 8 players I will feed them a player from the feeder to keep them at 8 players. Using this system I am able to keep the feeder game alive longer, without leaving the main tables too short. Once there is enough seats at the main tables for all players at the feeder tables I will move them all. At this point for the small game situation there is no longer a must move situation, and the floor is to keep table balanced. If a new table were to open again, we would be back to the last table feeding all the main games.
Hope this makes sense. I have a knack of complicating things, but for the most part it works out well. Hope it helps.