"King of the Hill"

That's what I wrote about – you need to stick to a week or less. If the King can't handle the schedule for whatever reason, he drops out, and a new pair is started. 3 days is still not enough; few people will be able to play at that pace for a long time.

You'll see, it will turn into a mess... like, I could play on Monday, Tuesday, Wednesday... but couldn't play on the other days, and my opponent is the opposite... and it turns into a mess.
I think we also need to introduce a veto option – like, after an opponent is assigned for the King, he tries to schedule a match with that opponent within one day, setting a specific date and time.