Normally, I allow the parents to raise one or two clutches and then remove that year's last clutch, sometimes their second, but most often their third clutch. We can then remove the nestboxes and discourage any further clutches. Bourkes would go right on raising offspring if allowed to do so.
In the house, where interior lighting simulates day length, they don't recognize that it's fall or winter and time to stop breeding. Our one-year-old hens are asking to mate now too, but won't be given a nest box until 18 months to two years of age. Until their mate checks out a suitable box for nesting, a male won't mate (at least typically they won't -- have yet to see an exception, but never say never).
About hand feeding Bourke Parakeets, the more you hand feed at once, the more difficult it is. I fed nine the first time, then let the parents raise some before taking out third clutches to hand feed seven more. It becomes difficult to keep the food warm and so I fed half, then made a second batch for the rest of them.
Got smarter with the second set of seven. We bought a small cup warmer by Mr. Coffee. It gets too hot, so I kept one small bowl of formula on it and one that wasn't. When one got cold, I could dip into the hot formula and mix some in with the other to warm it. Always test the formula so you don't feed hot formula to the babies. Better too cold than too hot. In fact, once the birds feather, it's less important that it stay warm. The younger the chick, the more important that the temperature is right...very warm, but not hot.
We also learned this year that our Bourkes love rice chex cereal. It's such a treat for them that I was able to hand tame some babies simply by offering it to them by hand. Of course, it helped that some of the hand fed babies were already eating it from the hand. We typically use spray millet in this way, but our birds are even crazier about rice chex cereal. Who knew!