I know what you mean. I've got mostly Dorkings, so they regularly brood, plus they're winter layers, so they're winding down production now even if they're not brooding. I've got 20 chicken hens and 5 turkey hens, and I'm starting to get more turkey eggs than chicken eggs!! But the 18 Dorking chicks are all vigorous and growing well under three broodies.
How many broodies you have depends on the breeds you have. Some breeds are well known to go broody, and once some start it seems to take over the whole pen. Other breeds rarely or never go broody. There's so many characteristics to consider when choosing a breed, and most people don't consider the tendency to go broody unless they specifically want broody hens. But brooding does affect egg production quite a bit, so if egg production is important to you than a few (or all) from a non-brooding breed might be a consideration
If you don't want the broody to raise chicks, you can break her brood over several days and usually get her back into egg production within a few weeks. I have posted an easy method for breaking a broody several times on this thread, at least once in the last month. Let me know if you can't find it and I will repost it if needed.
The eggs from times of plenty can last in the refrigerator for 4-6 months if properly stored, and eggs can be frozen for use during the lean times of the year. Let me know if you'd like me to post a method for freezing eggs that retains flavor and texture fairly well.