My understanding (for what it's worth) is that Marek's resistance is highly inheritable. That is, if you breed from a bird that doesn't show symptoms then you help breed Marek's resistance in the offspring. There's almost no chance of removing the virus from the surroundings as it survives for ages in dander and dust.
I also gather some birds can be 'carriers', but as the virus (once it's in an environment) remains infective in dust and dander for months or years, the question of carrier birds isn't really relevant. It's simply assumed the virus will always be there once it has arrived.
For this reason culling isn't likely to help, because the virus will still be in the environment. Excuse me if I'm wrong; this is just from general reading.
I would say you have the choice to either segregate eggs from the parent flock in a totally clean room (changing clothes, showering etc before entering the room) and then vaccinate the chicks as soon as they hatch (i.e. before they have any contact with the virus); or buy only vaccinated birds; or breed from any survivors that remain symptom free, and thereby produce your own Marek's-hardy strain.
Not an expert, hope this helps,
Erica