I left the experiment running for a few weeks, and then did not want to post stats that could bias the poll. But now we've got a good amount of data so I'm ready to post some results and make some changes.
Almost everything of interest is inconclusive, and most of what might be true is confusing. Here is the solid ground:
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!split was not used and the prevalence of multi-rooming was low beyond the first week.
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Activity on weekdays seems to have increased while weekend activity seems to have decreased.
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There were fewer large games.
As a result I will raise the room size to 32 player on Saturday and Sunday.
The least conclusive finding is the overall player count. Here is Steam average players:

Here are the site-generated unique daily multiplayer player charts:


It is all too noisy to say much, as activity is far too noisy. All I would say is from these stats is that the activity on weekends might be lower. We would need to run this experiment for months, maybe years, to see a change. So in lieu of clear player data, I have processed the battle size and duration data. The goal here is to find some changes that might feed into a mechanism that would say something about long term playerbase growth.

Here is the simplest stat: games per day. Overall there were more games. I only have the time at the moment to look at graphs and write, so I've done a count of the below- and above-median daily games.
| Days with above-median count | Days with below-median count |
Games of at least 8 players | 25 | 13 |
Games of at least 16 players | 21 | 19 |
There were far more "good days" if we just want games with at least 8 players, and about as many good days as bad for games of at least 16 players. But games per day is probably not the most important stat for playerbase growth.

Here is the number of hours covered by games of various sizes. I think this stat is indicative of future growth since people are more likely to stick around if they can consistently find a game. It is especially important for growing into weak timezones. Here is the same breakdown of under- and over-performing days.
| Days with above-median coverage | Days with below-median coverage |
Games of at least 8 players | 26 | 13 |
Games of at least 16 players | 16 | 22 |
Coverage is much better for medium games (8+) and worse for large (16+). But here is where it gets weird: the improvement is driven by weekday behaviour. There are 20 above- and 8 below-median days during the week, compared to 6 above and 5 below on the weekend. The weekend has better baseline coverage, but for some reason the change has brought the weekdays closer to the weekend baseline.

Finally, the playerminutes. See
https://zero-k.info/Forum/Post/271928#271928 for an explanation of this plot. What we can see now, with more data, is that the weekends were probably hurt by the change, while the weekday results are inconclusive. Saturday is was below the median six weeks in a row, while Sunday had two low outliers. This supports the depressed weekend indication from the unique player charts.
The unsurprising part of these results is that the weekends were negatively affected, at least from the perspective of playerminutes and running 16+ player games. It makes sense that, if there was little multi-room behaviour, then you'd see fewer games. The main point was to test whether we would see more multi-room behaviour. The surprising result is that the timezone coverage of the weekdays improved. For most of the week the 22 player limit is not even relevant. My best just-so story is that long huge games (22+) put a strain on lobbies via player exhaustion, and on weekdays there are too few players coming in to keep the lobby alive.
This gets us to the result stated at the top: raising the room size limit to 32 on the weekend. The weekend saw no significant benefit in terms of timezone coverage, and paid for it with reduced large game coverage and playerminutes. In terms of player preferences, 30% of the poll said they wanted to play larger games, so all else being equal, it seems fair to raise the limit at least some of the time. If we were seeing significantly more 16+ player games, then I would probably keep the limit at 22, since 16+ is already quite large, but that is not what we saw. Friday could go either way in terms of defining the weekend, but it saw a significant increase in 16+ games and coverage, so I will leave it at 22 and see if the trend continues.
Switching the rooms around twice a week is an annoying manual task, so I don't know how long it can go for without automation. But I would like to see if the weird result during the week persists.