Stability doesn't matter on a shotgun. Its a useless stat.
So, why not replace it with spread? Stability affects every other weapon, and for Fusion Rifle it affects spread and recoil of the bolts.
The higher, the more accurate/tighter the spread of a shotgun. This would affect hip fire spread and ADS spread.
Then replace stability benefits on barrels, magazine and traits with spread.
The following perks would become useful:
Smallbore (7+ Range and Stability)
Barrel Shroud (10+ Stability and Handling)
Corkscrew Rifling (5+ Range, Stability and Handling)
Assault Mag (15+ Stability and 10+ Rate of Fire)
Tactical Mag (10+ Stability and Reload Speed, 10- Magazine)
Steady Rounds (5- Range, 15+ Stability)
Slideshot (Sliding partially reloads this weapon and gives 5+ Range and Stability)
Threat Detector (Increased Reload, Stability, and Handling near enemies)
Stability Masterwork (10+ Stability)
It can also make balancing shotguns easier. The best shotgun is the one with the highest base range stat (and whenever its a Kinetic so it can be paired along with Luna's Howl/Not Forgotten)
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I don’t think buffing shotguns is a good idea