Local SEO, main page is already ranking in neighboring cities, should I still make a dedicated page for that city?

Hey everyone. I'm a small metal construction material manufacture in the South. I'm located between New Orleans and Houston. After the map pack my page ranks 3rd for "metal studs Houston" and 4th for "metal studs New Orleans" my main page includes a list of destination that we've shipped material to with New Orleans and Houston included. Should I just let this page main ranking page sit or also create a whole new page like titled "Metal Studs Houston" and "Metal Studs New Orleans" of course each with its own set of unique content? I'm afraid they might compete with each other.