Is the frame too small?. Well that depends on what you want to do. I´m 180cm, and so a 56cm frame should in theory be pretty much perfect for me. But being in my mid fifties, the sad truth is, that I get neck pain on longer rides, when using 56cm frames with drop bars. The reason for that, is probaply, that I prefer to be looking through my glasses, instead of over them. My favorite drop bar bike is supposed to be 58cm, but according to my measurements it´s actually closer to 60cm. This size gives me a fairly upright seating position, and this means that the only thing that hurts on longer rides is my butt!.
My winter/beater/grocery getter is an old Centurion that is around 53cm, and set up pretty much like your Miyata. It is actually a very comfortable ride for me, and surprisingly fast, actually it´s not much slower that my other bikes, if I put similar tyres on it. With drop bars that bike is absolutely unacceptable to my neck. So apart from looking silly (Just like your Miyata), that small frame is fine.
Based on my experience, I´d say, that if the Miyata is comfortable to you as it is set up, I think a 56cm or even possibly a 58cm frame would probaply be a good idea if you want drop bars and a fairly upright seating position. Of course a frame with a not too long top tube, would be best for this application.