I think it depends too on the timeline you are looking at. We have moved based on military transfers but always knew the earliest it would happen was July so that was the time frame I used as in daycare will end when the school year ends so families knew in January when we found out they were planning for summer. Guess it depends too on your area and how scarce care is so you take it when you get it. Also the opposite as in how competitive if parents are goaded into taking a space earlier by a desperate caregiver.
I agree on no lawn sign and keep renos as quiet as you can doing the out of the limelight things first - ie painting could be just because. At the same time if a parent comes out and asks you be honest. In most cases there is 60-90 days before closing so three months is plenty of time for parents to find care. They just need to know that you are not going to quit early on them too.