Commercial breeders often used to seperate eggs from different matings inside the hatcher by placing them in Muslin bags, or by placing them into small wire mesh container-like cages. I have managed to seperate eggs by making cardboard 'dividers' that contain the chicks as they hatch, however, it's as well to ring or mark the hatchlings as soon as possible as they are born escapologists and there's nearlly always one that very quickly seems to find a way out of it's cardboard corral, no matter how high or well put together it seems!!
I made some little wire cages to keep mine apart as I didn't like the idea of the muslin bags. Perhaps there's a way of converting one of the laundry bags that you put socks in. As Lordcluck says, you have to be very observant and have a very good secure system because they really are escape artists even in the first few hours. I use the tiny little coloured rings, put on as soon as possible. I always write on the pointed end of the eggs as that's the end that stays in tact during the hatching.
I put a cardboard divider in the hatching tray, then I use a pink highlighter on top of the head to deal with any escapologists! Usually though I hatch separately and raise in different brooding pens.