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.

There are surgical and non-surgical approaches to lip augmentation. Non-surgical approaches include botox (slight lift, reducing gum show) and filler (volume restoration). Surgically, you can have two separate incisions under the nose (italian), one incision under the nose (bull horn), one incision at the red/white upper lip junction (gull wing) or two separate incision at the corners, or a combination, depending on your desired look and anatomy. My preferred surgical technique is called the Elelyft, which is a version of the bullhorn approach. 
The ideal candidate for the Elelyft, or upper lip lift, is someone with a philtral length of 13mm or longer, no upper dental show, and/or a thin upper lip. The nasal base to mouth width ratio needs to be taken into consideration to avoid leaving the lip corners down.In your situation, to expose more of the upper teeth, a lip lift would be best for a long lasting result. Please review before/afters and my lip lift information page is quite detailed. Consult with an experienced lip surgeon for a complete range of options that are appropriate for your situation.
Gary Linkov, MD
Lip Specialist
Manhattan

You had botox to relax the lower lip?  That's not going to be effective for lifting your lip.  And, botox for the upper lip will almost always make that longer too.You attached three photos, but the key photo is to see your mouth open with your face relaxed.Probably you need a lip lift. This is done in the office and takes about thirty minutes.The link takes you to one of several articles I've written on the subject.

Thank you for sharing your question and photographs.  It appears that your best solution would be a lip lift procedure to help increase tooth show during animation.  Seek out a specialist in consultation to discuss. 

Botox around the mouth can be very tricky. Sometimes the results of even a few units can be amazing but other times little or no result is seen. Moreover, using too much can yield unwanted consequences. Fortunately though lip lifts are fantastic. The results are consistently good in terms of raising the upper lip to provide more tooth show with smiling and for giving the appearance of more fullness. The scar from the incision hides exceptionally well under the curves of the nose/nostrils. I would find a surgeon who has done many of them and get a consultation in person. Best of luck.