I'm not sure either what the fair thing to do is.
Someone who doesn't play many games doesn't deserve the title.
On the other hand, assuming a month of 8 games, a team with 15 players would only get 4 players out of 15 with 5 games, everyone else being 4 games, if the opportunity to play is spread evenly among teammates. This would give teams with only, say, 9 or 10 players, a distinct advantage for one of theirs to win the trophy.
Not sure what to do. One possibility (and I haven't checked how or how fairly it works out) would be to do average score list based on 60%, and total score not having any percentage requirement. Then the winner could be whoever finished highest averaging their two places.
The only place we could test this would be for January right now, but the list that is up for it has a 60% requirement for the point total too, so we don't know how it would look if that requirement were waived. However, on that list, only those with 7/8 or 8/8 games made the top 10; no one with 6/8 or 5/8, both of which are over 60%. So perhaps removing the percentage requirement from the point total list would have any effect at all.
Back where I started... I don't know what would be fair.
If we made the requirement 50%, then you'd have to play 4 games to have a chance as long as there were at least 7 games. It would lower the threshold to 3 when a month had 6 games.
Perhaps we could go with 50%, but give anyone with a higher number of games a boost to their average? For example, add 1 (2?) points to each player's average for each game they played. Then someone who played, e.g., 7 games instead of 4, would get 3 (or 6) extra points on their average. For computing, this could be listed as 'ave', 'bonus', 'adj ave'. Just a thought anyway.