Thanks for the positive comments, all!
I'm in Jamberoo, NSW, Australia - about 1.5 hours south of Sydney. It's classified as a temperate climate, and is some of Australia's best dairy country. I don't get snow or frost, and have good sun exposure, so can grow year-round. I think our climate is fairly similar to California from what I can tell. We live on 1 acre, so I've got a fair bit of space to play with.
Yep, the chickens get access to a bay for a month, before moving on to the next - so the vegies get 5 months of growing time. I'm finding some things (e.g. cabbage, beetroot, leeks) take the whole 5 months (or even longer) during winter. I'm going to protect them with chicken wire when the chickens get back into that bay, to hopefully give them a bit more time to finish.
Other crops are finished within 3-4 months (e.g. cauliflower, broccoli, snow peas, climbing beans), so as they come out I plant fast-growers like bok choy and radishes. During the final month, I throw chicken seed around and let it sprout - it gives the chickens even more greenery to eat when they get in there.
We're at the start of spring now, so the busy growing season is ahead. I'm going to experiment with moving potted fruit trees, blueberries, etc into the cages while they're fruiting - birds get all the fruit otherwise! They can go back outside when they're not fruiting.
It gets hot here during summer - we usually get a few days above 40 C (105 F), and lots of days in the 30s (85-100 F). I'm planning to cut sections of shade cloth to size and hang them in the cages using bungee cord. It should be easy to put up and take down as needed.
I'm preparing some more garden beds outside the caged area for crops that the birds and possums don't bother as much - potatoes, kale, melons, pumpkins, zucchini, herbs, etc. The cage space is valuable, so I really only want to use it for the plants that need protection.