I think now is as safe as it will get. Broody hens have been hatching and raising chicks with the flock for thousands of years. You are dealing with living animals so bad things can happen whether you integrate them now or later. Living animals don’t come with guaranties.
If you integrate now Mama will take care of integration. If you wait until she weans them the chicks will be on their own. The chicks will still have to take care of the pecking order problems, but they’ll handle that by just staying away from the adults most of the time. That’s assuming they have enough room to work with. If you have them shoehorned into a tiny space then they will probably have problems however you try it.
It sounds like you have a fair amount of space so I think now is the time to put the hen and chicks with the flock.