In my mind it is more important to schedule the doubles games first, and then worry about the distribution of byes afterwards. So after the schedule of play has been established, the rounds can be re-ordered to try to spread out the byes evenly. It is possible to do as you suggest and specifically optimize the byes, but it will severely limit the quality of the double schedule.

In some situations it will not be possible to have any schedule that is nicely balanced. For example with 11 players, you cannot have a schedule where everyone partners everyone else exactly once, in which case you need to state how many rounds of play you are looking for and what your most important objective is.

From your list, 9 players is the easiest because there is only 1 bye and this fits the standard whist design.

Here is an example from the Wiseman web site.

12 players should be possible by rearranging a whist design. If you follow the "pages that inspired the forum" link near the top of this page, then look for the whist table for 12 players. Now the objective is to reduce the schedule from 3 to 2 tables. Notice that the games (12 1 9 10) & (7 2 8 11) can be removed from rounds 1 and 6 to make round 12. Next take games (12 2 10 11) & (8 3 9 1) from rounds 2 and 7 to make round 13. Continue like this, and take one game out of round 11 to make round 17. Finally you can reorder the rounds to optimize the byes, but I fear that with a third of the players having a bye in each round, it will be impossible to prevent some players have consecutive byes.

I hope some of that helps.