Okay, since I'm using commercially available modern shot shells, it appears that the easiest means of tightening a pattern would be to use a shell with larger shot size in the second chamber all else being equal.
Yes on the larger shot but consider there will be less pattern density due to fewer pellets so probably wouldn't gain much, if any.
Mark, you could gain a lot by having the left barrel jug choked. Five thousandths off the wall thickness would give ten thousandths additional choke, making fourteen total. That would be a solid modified. I have had great experiences with jug chokes.
Two of my favorite "long range" guns are choked about what you have right now and they do reach out and touch 'em. Once I got over worrying about numbers and observing the kills I gained a lot of confidence in having little choke.