Not really flawed, the amount of daylight has an effect on hormone production and eventually the darker conditions would decrease those hormones, but, it would take weeks for this to work.
With my horses, for me to get my mares ovulating so I could breed them in April to get March foals (11 months to carry a foal), I needed to start around Christmas time and keep lights on in the barn in the evening for an additional 3 hrs - and the light had to be a certain brightness - enough to be able to read the print in a newspaper - so fairly bright.
Same thing if I wanted show horses to shed their hair earlier in the spring.
Now with the chooks I have read that increasing light hours will increase hormone production, and I was wondering if the lighting I now left on each morning as I am up so early for work, had an effect on the pullets starting to finally lay eggs.
I like your idea of reducing light to control ovulation, it just would need to be done for many weeks to see any effects. If it were me I would have a small room for them all to go in so they were together if you are worried about them being apart. Is there anyway this can be built in your hen house?