I have a slightly less intensive program for my chicks, and at 7 weeks old, I haven't lost any! Also, it seems ( I have no idea if it's actually true) chicks hatched by my broody seem to have a more natural resistance to mareks then brooder raised chicks, so, yes, definitely give the chicks a chance!I agree 100% with everything saltandpepper said. If the chicks are not sick, don't put them down. Depopulating isn't going to work for you. The virus can live for years in the environment. You could completely clean your coop and wait for two years, get new chicks and they could still become sick.
Not to dash your hopes, but often times my "strongest and biggest chicks" are the first ones to die from Mareks. I had a huge, dominant cockerel that was my first cockerel to die. The smaller, timid one lived the longest. He actually got to breed with the hens and died at 6 months old. I had 2 pullets that were raised over the winter by a broody. One pullet was small and sickly (coughing all the time). Her sister was twice as big as she was. One day she got sick and died two days later. Little sister recovered and is now laying eggs.
If you have chicks that get sick, cull them before they are suffering. I'm not sure why your state vet is trying to convince you to cull everyone now.
I buy my own vaccine and vaccinate my chicks. You can buy vaccinated chicks from a hatchery. That might be the best option in your case if you don't mind getting hatchery birds. It sounds liken maybe one of the limited breeders in your area is selling birds from a Marek's infected flock.
What I do with my chicks is vaccinate at 1 day old. They spend the next 3 weeks in the back bathroom where they are not exposed to any other birds or shared equipment. They have their own feeders, bedding, etc. I feed them first in the morning after I shower and change my clothes. Then I go out and take care of the other birds in order of age. One month old pullets get fed next, followed by the adults in the coop. I know my house is infected with Marek's since I had 2 sick birds living inside for a month before sending them in for necropsy. I realize my situation isn't ideal for the birds, but I'm doing the best I can.
When the chicks are 4 weeks old, they are vaccinated a second time (it is part of my vaccine experiment). They are moved into the living room where they are handled more and the "biosecurity" is reduced quite a bit. They still have their own brooder, feeder, bedding and food. My objective is to slowly introduce them to small amounts of the virus so their immune systems can become stronger before they go into the flock.
At 6 weeks they start going into an outdoor chicken tractor during the day. It is in a part of the yard where the other birds don't normally go, so I'm pretty confident they are not getting huge doses of the virus. Over the next two weeks the tractor is moved so that it is closer to the main coop and all the other birds. At 8 weeks they are allowed to free range for a small period of time with the flock. By 10 weeks they are (hopefully) fully integrated with the flock and have had 10 weeks to build immunity to Marek's.
Currently I am hatching every 4 weeks. It is very labor intensive to have all these chicks in the house plus two tractors outside. I'm doing one more hatch and then I'll take a break until fall. I will have five batches of chicks that have been vaccinated, and, and two batches that were not vaccinated (only 3 pullets left total since all the others have died).
The other thing you can do is get older birds. Last year I got more than a dozen adults and none of them died. By the time they are a year old they should already have natural immunity to the virus. Don't cull your babies though...give them a chance!