I do not know if brown leghorns will become broody more often then whites or not. I wish you well. I followed all the direction there except I never sprayed the eggs with water after the 16th day, even in Utah, and fed the broody hens only grit and scratch grain while they were setting. You can get birds to go broody even in the winter time if you can put them under at least 14 hours of artificial light a day, and provide them with a suitable secluded nest area. Once they go broody they stop laying.
Leghorns are probably the worst breed to try and set eggs under.
I have had very good luck with Show quality bantam Rocks. I also got some mongrel Ameruacanas from Murray McMurray to go broody. I have heard that Silkies are the best mothers. You can induce broodiness by supplying environmental stimulation. For bantams I would separate the hen that I wanted to go broody into an isolated cage with a nest box.