Thanks for the summary.
As I am an admin in multiple groups and usually responsible for vote chess in them, I can organise vote chess games and I can even get those clubs to play against this team, so we would have good opponents on both side.
The only issue is that I cannot write a challenge and accept it too and I cannot be present in both teams to admin.
In some of my bigger teams, it is not an issue as I can ask another admin to accept it.
On the other hand I can organise challenges with other then my teams or if we have at least another admin here, then he/she could challenge and I can accept. 
My point is, I am happy to help and create vote chess games and/or take on other admin tasks if needed and trusted by them, but ideally we would have at least one more person to help out in those special cases mentioned above.
Part One: how many - how often?
Our KIA inc Club Vote Chess games are intended to be instructional games for the benefit of all of our members; advanced and beginning players and everyone in-between.
The ideal is to provide a steady flow of tutorial activity without overwhelming those who participate. The formula I have found which works best is actually quite simple - start one new game each month.
After a month at three days per move we will have made five moves.This is usually enough that the game will have assumed a distinct variation, although still in the opening phase.
It is then time to start another game.
In another month and another five moves, the first game will most likely be entering the tactical phase. Then on to the middle game, the late middle game, the end game, etc.
The average vote chess game lasts between six months (30 moves) and eight months (40 moves). Many games are shorter due to time-outs and aborted games. In practice this usually results in an aggregate of about six games running consecutively, all of them in different phases. This keeps it interesting. The Vote Chess participant will constantly be seeing how the KIA works at different phases of the game.
Part Two: what day to start a game?
If we are not careful in scheduling, the situation could easily arise when it could become our turn, in all of our games, all on the same day, or on nearly the same day, resulting in a frenzy of activity followed by doldrums days wherein nothing happens.
To avoid that kind of logjam, I have been starting new games according to a schedule using a calendar software based on the six day turn around of 3 days per move.
When it became that time each month, to start a new game, I could simply check the calendar for an open slot (day) and then submit an open seek on the morning of that day, and usually have a game underway vs a good opponent by that afternoon.
With a new game starting each month and a new position to analyze each day, like a daily puzzle, we have instructive games in all phases and spread out over time making our Vote Chess program more interesting and instructive for all who follow and participate.
I have done it this way successfully for several years.
But times have changed.
Today Open Seeks are overrun by absurd challenges and low rated, one-person teams taking open seeks. If we are going to have meaningful instructional games then we need to find good opponents. And finding them is the easy part.
Once you have found a suitable opponent, do you just send a challenge? And what if they don't accept? How long do you wait for a response?
I think the best way is to contact the club in advance and ask if they are willing to play and that we will be the one to send the challenge on a day of our choosing. It might mean days of back and forth discussion but since a VC game lasts six to eight months, I believe it is worthwhile to make this preparation.
But right now I just don't have the time. I don't play the KIA anymore. I never did play it very much. For several years I have been maintaining this club simply because of the people who enjoy these games.