You don't have to move her.Do you have to remove her from the flock? She has the one nest and will let other go in a lay eggs as soon as one pops one out she pushes that chicken on and lays back down on the eggs.
I was thinking about marking the hatching eggs.
I, and many others, just find it much easier to manage if they are separated by wire from the flock.
Definitely mark the hatching eggs, then daily remove any others laid in the nest.