This would be okay with me. That is, a player may choose to intentionally use a “extra day” to postpone the deadline (even if they have already submitted a move) by informing the arbiter (via the private PM) before the normal deadline. Note: the deadline in each round may only be postponed once.
If there are no strong objections from others, I will add it to the rules.
Another note: a player may (but does not have to) publicly announce that they intend to use an extra day, but that is not binding and not official. That is, they must also withdraw their move (by PMing me) or fail to ever submit one in the first place. If the round is extended, I will publicly announce which player(s) are docked an extra day, but not elaborate further.
Once a player actually misses a move (by missing an extended deadline, or missing the normal deadline after running out of extra days), I will let everyone know that the player has gone absent. If I do not get indication from that player that they intend to continue playing, I will seek a replacement player for their position. If they continue to miss turns, their moves will count as passes, and I will assume that they vote for resign and for any draw that excludes themselves. Basically, starting after the second consecutive missed move, they are temporarily eliminated (for the sake of resign/draw voting), but with their stones remaining on the board, such that a replacement player may join to take over their position. With significant reassurances, I may also choose to allow the absentee player to resume their participation. Hopefully, we won’t have to use these procedures, but I just wanted to make it clear.