They are experts and you can see them through the MDA clinic in Rochester. I can't think of anyone closer to you. You can check some of the other PPA doctors on the left side of the menu.
Strabismus has been associated with myotonic muscular dystrophy, but it's not quite as clear how common it is with myotonia congenita. My granddaughter with MC has it, but so do many normal kids.
Quinine sulfate is the oldest treatment for myotonia and is hardly ever prescribed any more. Since you're in the US, you should be able to get a prescription for Mexitil, which is the most effective and seems to have less side effects than some of the other medications like Tegretol, Dilantin, and Diamox. You will need a cardiac workup before starting Mexitil and you have to start with the lowest dose and work up gradually.
Please let me know about your experience if you are able to get in to the Rochester clinic -