Tires might make a slight difference. Drop bars can make a difference, but not much at those speeds. I don't think there's anything you can do to the bike that would get you more than 1 mph.
I'm not an especially fast rider, but I slow down a lot when I ride with my wife. The rides are very enjoyable, If I want more, I ride another 10 or 20 miles after our 'couples' ride is done.