I'm not sure what you mean by "culling". Culling means to select. It does not mean to kill. Some people cull by giving chickens away or selling them, separating them into breeding and laying flocks, or sometimes by killing unwanted chickens. Sometimes culled chickens that are killed are eaten. I'm going to guess you mean that you plan to eat the chickens you cull.
Depending on the medicine in the medicated feed, there can be a withdrawal period from when you stop feeding the medicated feed to when you should process the bird. You need to know what the medicine is in the medicated feed so you can determine what, if any, that withdrawal period should be. You can e-mail or otherwise contact the feed manufacturer to ask them. They shoulkd know exactly what they are putting into their feed.
The way I get around it is to not feed medicated Starter at all. I don't know why you are feeding medicated feed? Are you treating or just preventing? Do you have a history of some disease you are medicating against?
I keep my brooder pretty dry and feed them dirt from the run at a very early age to introduce anything that the adult chickens might have so they can build up immunities. I have not had problems with coccidiosis or anything else. We are all different. Some people have a history that says they need to feed medicated feed, but I don't. So I don't feed medicated feed at all.