What we could possible implement is that you can send a private replay but it only appears on the scoreboard when public days are over.
I like the idea. It would be a good compromise - the annoyance of counting down the days feels rather excessive if you are not going to send public replays anyway. And it would add another day to wait for during the month
Technically, an auto-reveal of replays would be needed for it to work well; I guess dreadnaut would have a couple things to say about that issue (cf. the plans for auto-revealing at the end of the race).
