5-day notice on the 2nd day?

[Uwe K.]

So here is a thought I had:
If rent is due on the first, and has to be received on the first, couldn't I give the cure or quit notice on the 2nd day?

Background:
Currently my rent is due on the first (postmark) and must be received by the fifth to allow for the mail truck to create some USPS deficit. If not received, I can send the notice on the sixth. So far so good.
Last Nov. I had a situation: Tenant didn't pay (I knew it beforehand, she told me that she moves, aka breaks the lease, and needs the money for the new place's deposit. Nice logic...
So for whatever reason there was a delay in giving her the 5-day cure or quit notice of a few days. Then the fifth day was a Sunday, which added another day, day 6. On day 7 I filed, only for the court lady to tell me that the next possible court date was something like 2 weeks out, ended up Dec. 3rd!

IN this case I was 95% certain she would leave, which she did. Also did not show up in court.
But now imagine she had not left. Court writes a writ for 5 days, that's the 8th. She is still not leaving. then on the 8th, maybe 9th I go to the sheriff. Our sheriff is apparently currently too busy with making TV commercials for injury lawyers, so it takes them the max. allowed time of 10 days to kick the people out. By the time I get my property back it Santa is coming to town, which is a ridiculously long time, even without my own delay for a few days.

So I was wondering of changing some tenant's terms to say I will go and pick up on the first by, say, 7 pm. Then if they don't have it, I can give the notice on the 2nd and save 4-5 days of "kick out lead time"
There is nothing about a required grace period in the state statutes, and I don't have to allow x days for mailing.