My girl does this! It's super annoying, but we know all her egg hiding places now, so it makes it easier!
We haven't tried leaving fake eggs, but it seems to work for a lot of other people...
I try and keep my layer in her pen till 9-10am (after she's normally laid for the day) and then let her out to free range till bed time! Depends on your set up if that's actually possible tho! Haha
Mine lays REALLY early. Like around 7:00. Is that normal?