Hello,
Perhaps the subject has already been discussed and if so, I'm sorry.
Would it be possible to create a league cup?
All the cup winners would meet again in a mini-tournament the following season. Very simple principle on paper.
Before I fall over myself, in terms of the calendar, the ideal slot is during the break (for example, there are others).
It can be done quickly with 1 match every 2 days.
Conventional but not excessive.

Enjoy the game.