You may be interested to know that what I'm currently reading (which is written for the poultry industry, not by anyone hostile to it) says that production breeds are deliberately overfed simply in order to get more eggs out of them. Here's a choice bit: "the pullet appears to have a fairly precise innate ability to regulate its energy intake regardless of dietary energy level (Cunningham and Morrison, 1976; McNaughton et al., 1977b; Doran et al., 1983). Manipulation of energy intake is, therefore, best considered in relation to feeding management and, in particular, methods of stimulating feed intake. For example, feed intake may be increased through use of pelleted feed, increased frequency of feeding, feeding at cooler times of the day, and, where possible, use of longer periods of light".
So pelleting is a device to over feed them and enhance egg production, like artificial lighting.
Yes there will be bickering - it's the pecking order - but if you can wait till those who go first have filled up and moved off, and then replenish the bowls for the next sitting (and so on, as many as it takes), everyone gets as much as they want, and then at your place they can also forage all day to top up. Worth a try surely?