RE: Full or Super full choke?
 

Whatever gun/choke you end up with, be sure to determine where the "center" of your pattern is hitting relative to your point of aim. You do this with a large piece of paper, like 3' x 3'. Shoot at a small dot in the center of the paper. Then look at the pattern. Is the highest concentration of shot high, low, left or right of the dot? It is not uncommon for it to be somewhat off in one direction or another from where you are aiming. You can compensate for this by aiming differently or by using an adjustable sighting system.

After you know where your gun is hitting, you can then think about your pellet count in a 10 inch circle.

RE: Full or Super full choke?
 

I agree with UncleNorby. Try putting an aiming point on a large sheet of paper and draw a 10" circle around the area with the most hits. I bet your count will go up. Adjusting the sights could help a lot. Using hevi shot will probably also increase your pattern density as will polishing your barrel. Also, as someone else mentioned, #2 shot is not legal in many states. Check your regs.