Tad, a choke can be installed. Perhaps your gunsmith meant that he didn't have the necessary tools for him to do it.
I know that some powders pattern tighter than others, Green Dot being one, velocity of the load, size of the shot, even the type of shot, magnum shot is harder than chilled shot so it doesen't deform like chilled shot, you tighten up a little that way, type of wad makes a big difference.
There is an entire chapter in the Lyman Shotshell Reloading manual devoted to pattern control. I highly recommend the book, it's not very expensive and there is a lot of information that you're looking for.
I don't think you'll ever get it to shoot like a Super Full Turkey choke, but you can probably get it to do what you're trying for.