If you are shooting with #4 shot you may want to drop down a size or three. Try some #5 (my favorite) or #6, 7 1/2 with a choke in the .660-.665 constriction range.
When we did some pattern testing several years ago with Remington barrels, we found that a couple of the realatively cheap Remington turkey chokes patterned better than some of the high dollar after market chokes. My 11-87 loves the Remington Turkey extra/super full choke with a .665 constriction and #5 shot.
To increase the number of shot in your pattern, #6 or even #7 1/2 will more than do the job out to the 30-35 yard range where you normally shoot turkeys. Before spending a bunch of money on chokes, try some of those shells with your current set-up.
Also if your shooting at a small target get a large peice of cardboard for backing,you would be suprised at how far off the target some guns pattern,you may have a great pattern but most of it missing the paper,I had to put adjustable sites on a 24" barrel to correct it for me,others shot it great ,no 2 people hold/control the guns the same .
What type of sight are you using on the gun? Is a front and rear sight or the bead on the barrel? If it is the bead you might need to consider an aftermarket clampon type of sight. The ones with a rear sight and a front sight work really well. You can pick whichever flavor you want. Some are just a front bead and a rear bead some have a rear buckhorn (Like a rifle) some have sight rings in the rear. It doesn't really matter which one you choose.
If you already have the two piece sight, then you will need to shoot at a very large target. Then adjust the sight to make the thickest or most dense part of your pattern line up with the sight. Follow the directions on the sight for adjusting. If you no longer have the instructions let me know. I may be able to help you with that.