There are 365 days in a year, and if your hen molts quickly, she will be out of production 30 of those days. If she spends 2 months raising a single clutch of chicks, she is down to 270 days left in the year. Throw in raising a second clutch of chicks, and she has only 210 days to lay the 220 eggs you want out of her. Is that what you meant?
If one breeds for birds who have a quick molt recovery and also molt late in the season when there is a natural slow down anyway, there shouldn't be a 30 day lapse in the laying cycle. A slow down, for sure, but not a total lapse. Those are traits that can be bred for.
If you want birds to take it easy on your delicate soil, why do you want them to hustle for their food? I thought hustling chickens meant scratching chickens, which are hard on the soil and plant roots, and the unwanted pests in the soil. (I have used my chickens to reduce the scorpions in my yard. Worked pretty well, but they left a lot of poop in inconvenient spots. In other years, they scratched up and ate all my new daylilies.)
Actually, the scratching aerates the soil and, unless one is overstocking any one area, the chickens shouldn't be doing that much damage to the roots. The only time chickens are going to damage soil and pasture to any degree is if they are heavily overstocked in one area.
Best wishes,
Angela