When you say "A LOT" of bread, can you quantify this? Bread is low in protein compared to chicken feed, but chickens love it, so they will fill up on bread and eat less chicken food, resulting in less protein in their diet, which is what they need to produce eggs. It will also lead to them becoming obese over time which will not only impact on egg laying but also general health.
That said, your chickens didn't all stop laying overnight because they suddenly became obese or have a bad diet but there may be another environmental factor which is making the lower protein diet more of an issue. Mites are the first thing that comes to mind. If mites are sucking their blood at night and they are already low on protein, that would cause problems and mite populations can explode very quickly in summer heat. My advice would be to stop the bread, perhaps switch them to a higher protein feed and check the coop for mites. I've been battling them in two coops this summer but other adjacent coops don't seem to have a problem. It may be due to different construction or materials or how the sun hits it, but it is certainly possible to have a problem in one and not the other. Excessive heat will also knock egg production and if hens are overweight they will struggle more with the heat.
I should say that I am not saying your hens are obese, but just that it might be a possibility if you have been feeding them lots of bread over a long period of time.
Another possibility is rats or other vermin taking the eggs.... I've had a problem with both rats and jackdaws this summer.
A third possibility is that they are going into moult. I have a few that have started moulting and egg laying has dropped off. My hens are all different ages, so they moult at different times. If yours were all hatched at the same time, they will moult about the same time. I can't remember if you said how old they are. Also are the Americaunas next door the same age or younger? If they are younger they may cope better with the heat.
There are so many minor differences that can have quite a major impact, but you have to look at the details to see them.