It can be quite damaging for the chicks to get too much calcium and protein. Too much calcium will damage a chick's kidneys. Too much protein and they won't have the steady, even growth you want for strong bones. Are they in a dirt run the whole time? They need a source of greens. I'm also surprised you're not dealing with bullying. Maybe your run is huge? Can you separate them during the day so each group gets the appropriate food? Even one more month would be a good idea.
I know that plenty of people have chicks that are cared for by a mama hen, and they free-range together with the laying hens. But, mama usually keeps the chicks away from the others, and they're out on pasture, so not guzzling down on laying hen feed.
BTW, the chick feed won't hurt the laying hens, but they won't be getting all of the nutrients they need if they eat just that.