Is there a way to contact the general manager through direct email without going through customer service?

No they avoid customers

If you are a regular customer you should ask for them next time you go to that store. If they avoid you when you are in the store they manage it is a clear sign that they are either avoiding you, not at the store or too busy to see you. They can only avoid you for so long. You are always going to go through customer service when you call into a store because they filter out calls that way. Wish I had a better answer for you but unfortunately this is the way large stores/companies operate. Email, definitely good luck with that.