Welcome to the forum. When I removed the AIS it didn't help the backfire, but the AIS should be removed anyway. I have BigShots too and the AIS removed, when I added the Power Commander III and used the V&H BigShots - Stock Air map the backfire was almost gone. Only a rare backfire. Since I have added a Churchkey and changed the map it now backfires a bit more, yet not near what it used to. I may need a custom map.
In addition you will want to learn to control the throttle better, that helps too.