You overthink this. (Be sure to read the last two paragraphs).
First, promoting your own games goes without saying. You already do that implicitly, by being the creator. People see what you have also released. And if they do not look, why should they be interested in advertisment/promotion for other stuff on your game page.
Second, that is actually, what itch is for. The have "related games" on each game page that appears after a while. Also, recommendations. Stuff like, you might also like, pops up after downloading too.
And third, how to even group games together. Just because I liked your game does not say, I would like some random games that are only grouped together with your game, because they are in some obsucre arbitrary list. Or that I would like to see your promotion.
Even more so, if those two or three other developers have nothing at all in common with you. No cooperation, no joint efforts, no linking qualities, other than, I promote you, you promote a, a promotes b, b promotes ... and .... and z promotes me.
I ve seen team ups, but those x-promotions were more because of the previous team up, and as such to be expected.
That being said, the easiest way would be a public collection that each developer could maintain. Some, games I recommend to try out collection. Or even a title with reference to that x-promotion project, so people do not think, that those games are collabs. The titles could be slowly switched 1 each month or so. Do it too often (or at all) and you anger your followers. And if the collections get too big, it defeats the purpose. If it is 100 games, one could just use itch's browse instead.
But yeah, the hardest part is to enforce the fight game club's rules. There are those that take more than give, abandon their project, and are in general not self concsious about the quality and importance of their games. Or overestimate their commitment to any such promotion activity.