The slaughter of a person who leaves out Salaah

Some principles that should be agreed on. (If they are wrong pleases tell me). Halaal food is extremely important. A body nourished with haram will not enter jannah. Hadeeth: Even the slightest doubt of halalness of food will render it haraam for you. We should strive to follow our religion even if its hard on us. A person who doesn't pray is a kafir. Most of the ummah think if they don't pray they are still muslim. Most muslims dont pray (Stats). Being a muslim is a requirement besides saying bismillah allahuakbar. Due to these points, I am in doubt of the food that is sold and they claim it is halaal. There is a great chance the food I eat is being slaughtered by a "muslim" who doesn't pray which puts me in doubt of its halaal status therefore it's haram for me. Does this seem extreme? Is this against the Sunnah? Please provide evidence and suggest what I should do?

P.S. I live in a Muslim country and I went to a chicken shop who slaughters the chicken on the spot. I came to know the man is known to not pray at all. Therefore I cannot trust the government which is appointed to make sure the meat is halaal. Also is it enough if the food I am eating has a halaal label on it?