What procedure would allow me to show more teeth when I smile and speak? (photos)

Your upper lip is too long and the technique I recommend is a lip lift.  A lip lift does 4 things: shortens the distance between your nose and upper lip, increases the mucosa of the upper lip, increases the incisor show and pulls up the corners.  Best Wishes,Gary Horndeski, M.D.

A lip lift is an excellent way to shorten the philtrum and increase tooth show when you smile. This procedure can be performed using local anesthetic and a small incision under the base of the nose. Recovery is usually just a few days and visible scarring is minimal. Results are permanent. Make sure the surgeon you choose is both board certified and highly experienced at performing lip lifts to ensure your results are optimal. 

There are 4 pairs of muscles that influence how you smile, look at a Youtube video titled "Muscles of Facial Expressions (Origin, Insertion and Function) - Anatomy" starting at about 8:18 describes them.
When you smile you are pulling mostly with the risorius and the Zygomaticus major. To show more teeth centrally you would have to pull with the more central muscles (Levator Labii superiors and Depressor septs nasi- this one also pulls down the tip of the nose). You can train yourself to do this in front of a mirror. Actors do this training to play historical roles to mimic the persons expressions- it works, but takes a lot of practice and I suspect some people are better at it than others.
The other answer of course is surgical shortening of the philtrum. Check out in the link below for results in males to see if this is for you. The video below also shows surface anatomy of the lip and how it relates to surgery.