Sounds like a good plan. Sorry for stating the obvious. It's always difficult to tell how much knowledge/experience people have.
I have to say, there are endless hours of fun to be had watching nature at work with a broody and her chicks and would definitely recommend it over an incubator. It just does your heart good to see her teaching them to dust bath and roost for the first time as well as all those cute photo call moments when fluff butts are climbing on broodies back or popping their heads out from under her wings.
Of course you also have to be prepared to deal with the unwanted cockerels.... I'm rapidly approaching that point from my first brood. They are barnyard mutts, so no hope of a breeding home for them and sadly they will be going in the pot. I'm dreading the day of reckoning, but they are starting to fight a bit now and there are 7 of them, plus my existing rooster and whatever males I have in my 2nd and 3rd broods, which are still a bit young to tell. I struggle to kill a fly, so it is not going to be easy!
Anyway, good luck with getting a broody. It might be worth asking around locally specifically for a broody rather than buying any hen that is of a broody breed, as some people don't want them and spend a lot of time trying to break them (my neighbour is such a case). A straight swap for one of your egg machine leghorns, might even be possible. Just an idea.
Best of luck finding the right hen and having lots of chickies next year.
Regards
Barbara