Ruger Super Warhawk modded to burst fire, with smartgun. Fill remaining slots with RC mods.
I got the impression from the OP that the character was an Automatics specialist, and wanted a Machine Pistol because it would use the Automatics skill instead of Pistols. Your burst-firing revolver (and I'm not even going to get into how logically impossible that would be) would still be classed as a Heavy Pistol.
Also, with a Large Firing Selection Change costing 4 mod slots and Smartgun System and Skinlink being 1 slot each, there would be no slots left for recoil comp.
If one were truly dead set on having 6P of damage, one could add High-Powered Chambering to a machine pistol. Costs less slots, and the ammo capacity wouldn't have shrunk to "2 bursts and then you're done."
AFB at the moment but I believe gun heaven has a clear winner thats basically a full auto heavy pistol. Can't for the life of me remember what it was called though.
Just skimmed through both Gun Heavens again. Saw some machine pistols and burst-firing heavy pistols, but none that struck me as better than what was in Arsenal.
The best burst-firing heavy pistol, in my opinion, is the Ruger Thunderbolt, since it comes with two points of inherent recoil comp and it would only take a couple mods to make it nearly recoil-immune. But again, it would use the Pistols skill instead of Automatics, and I think the OP wanted a gun that used the Automatics skill.