Since they are slow growing and disease prone, most nurseries are probably reluctant to handle large sizes. You could hire a landscape company to extract a 10 ft tree with a machine that creates a ball from the forest up north for a nice chuck of change. Not sure if they are able to be transplated.
Porcupine Hollow Farm in Mason Michigan has native white birch 800-568-9179. Ray Wiegands Nursery in Macomb might have them. Torre & Bruglio 800-996-1692 & Vidosh 248-335-1123 are commercial landscape companies that would be able to handle a large birch trees. Working at Vidosh, I plant about 10 12ft pine trees a day with a backhoe.