While lengthening your upper teeth might give you some improvement you should visit an oral surgeon to see what can be done to improve the proportions of your upper jaw so that more teeth show when you smile. Jaw surgery may be possible. Less extreme though, botox has also been used to relax the muscles around the mouth so that more teeth show when smiling. Consult with your cosmetic dentist and have them do a digital mockup and refer you to the appropriate specialists.
You are right about the size of the teeth. Your upper jaw did not grow down enough. What you can do is have jaw surgery and being the top jaw down. The procedure takes about 2 hours.