I house mine together... but keep only breeds that lay a different color. I swap my roosters in or out according to what I want to hatch and then collect only the correct colored eggs.
OP, if you try the die... I might do ONLY the Orps or only the non orps if I was at all concerned with the die effecting hatch. The food die shouldn't have much effect, but the lipstick might clog some pores.
Another alternative... Just lock your Orp hens into a temporary set up. Their eggs will be fertile for about two weeks.
Personally I will NEVER buy broody hatched chicks... too much chance of disease. Hopefully you would let the broody raise them before selling them off. Some people let their broody's hatch it up but never let her keep the chicks, which is downright cold blooded to me.
Don't forget to set all the eggs you wish to hatch on the same day. If you DO hatch some non Lav Orps... it will be obvious at hatch by chick color. You could always dispatch them or sell cheaper than the Orps.
Good luck!