How about this random idea: the problem is that there are already too many matches, not too few! The repetitiveness of the league is finally causing more and more people to simply not go.
So,
how about having teams play each other only twice in the league, regardless of the size of the league. But, double the admission price! This not only means that there could easily be a winter shut-down, but also that each game would be much more of an event (or a non-event, but even so it would be more of an occasion). And the enthusiasm among fans might return after a Dec-Feb break.
It wouldn't cost fans any more in the long run, but might even increase income from hospitality, catering, etc.