As I said, I don't have them, so just repeating what I've read/heard. Storey's guide is here
https://archive.org/details/Storeys_Illustrated_Guide_to_Poultry_Breeds_Complete/page/n161/mode/1up?view=theater&q=silkie
I assume lay rates are calculated for the year, so even if they lay a lot between...
You could use golfballs as fake eggs instead, then there's no risk of confusion, they won't go off and explode over time, and they will work just as well as a clutch of real eggs to stimulate broodiness.
Be patient.
What you are already doing is the traditional method: leaving a clutch of eggs...