One of the most important things you can do to improve the performance of any shotgun is to "Deep Clean" the barrel.
It takes a little bit of time but will pay dividends in improved patterning ability. It can sometimes save you a good bit of money by allowing you to use the same choke/shotshell combination that you have and see a dramatic improvement over previous results.
I originally developed this procedure for the many 835/935 shooters who inquired about how to get better patterns but it's applicable to any brand of shotgun.
Please try this and see it works as well for you as it has for hundreds of others. Here's a link to the article describing the procedure.