If you try to switch diet by withholding food, of course they may abandon the eggs or even worse, hatch them and starve all but one chick. However, I found that when my birds have babies, they are MUCH more likely to eat a variety of healthy food, and feed it to the kids. I first noticed this with my tiels - one mom who previously ate very little except for her seed suddenly began hanging on the cage bars and screaming, if I was late with her fresh food in the morning. When I fed her the fresh food, she'd stuff her crop and run in the nestbox to feed babies.
It's the same pattern with my nandays. When they're breeding I feed the same amount of seed as usual, but in addition, my guys go through about 2 cups fresh food a day. I feed a sprout mix (supplemented with calcium), cooked grains/beans/rice with all kinds of shredded greens and veggies, healthy bread, cereals, and pasta, some scrambled egg or well-cooked fish/chicken, and as much carotene-rich foods as they'll eat. They pick whatever they want, and feed it to the kids. Sometimes they feed them greens, sometimes lots of sunflower seeds, sometimes nothing but rice, but it all balances out. Their babies are beautifully healthy.
>> Since your birds are sitting on eggs, this may not be the right time
> to switch their diet even though the chicks of course would benefit
> from a healthier diet of their parents. My thoughts behind this are
> that the birds may instinctually destroy the eggs if they fear that
> there is a loss in food reliability. Let me explain, a little later