Due to how a carronade fires in a cone pattern, using lesmok allows for longer range, but when an enemy is that far away, the cone is incredibly spread out, making it so that only a few of the projectiles hit the target while the rest pass all around it.
If you want range, use heavy clip, that way it doesn't shoot in a cone, but rather a beam. You can take out a balloon in two shots at gatling range.
Greased lets you shoot faster, but that's still only two shots which already fire within a second of each other.
As for burst, I think it only affects weapons that explode with an AoE like Mortar, flak, Lumberjack, mines, rockets, etc. I don't think they affect direct hit damage weapons like the flamer, gatling, and flare. Though someone else will have to clarify that.