Just flown this route with Scoot, stayed 3 hours in Singapore. Though I do have a Non O visa.
Overstay should not cause a problem. It’s only when you get picked up by police that they can then deport you.
As for coming back next day, that is down the IO. If he thinks you are living here and border bouncing to stay here, eventually they will ask questions
Great news. The reason why this is the best is because you get concise answers, then comments are closed to stop it dragging on and then giving mis information