Just like the title says, there are a couple distinct changes that the shotguns need to be competitive alternatives to the SMGs. Before I say anything else, the fact that their instakill range is very short is NOT the problem. If the instakill range was simply made longer then we'd suffer a problem felt before- that a shotgun user could make instakills without having to even aim at the target. I view the real problem being the relative ineffectiveness of wounding blows from shotguns. Shotgun use should (in a more ideal situation) most often fall into their 2-hit-kill range. Blam, ch'k ch'k, blam. But in close quarters a wounding blow still allows the target to retaliate to a point where any time when your first shot fails to kill, you're screwed.
Therefore, my suggestion rests on the principle of making shotguns more practical when you're gunning for 2-hit kills.
Necessary change #1: All shotguns need a proficiency to improve the speed at which they cycle the pump-action (lever action in the case of the M1887, fire cap for the semiautomatic Striker, and general fire rate for the other two). The more simple answer would have been just giving them all the rapid fire attachment, but having this in conjunction with proficiencies like range and damage pushes things over the line. Therefore having a newly made proficiency to improve pump speed is the best fit for this situation. 'Double Tap' sounds like an appropriate name for this. As one final note, don't have it unlocked rediculously late. Its enough trouble unlocking any useful proficiency for the shotguns as is.
Necessary change #2: By default, all shotguns' survivable wounds need to in some way temporarily cripple the enemy in a way that ordinary damage doesn't. It would be too much if shotgun wounds had all the same effects as a stun grenade, but that's is on the right track. It would probably just restrict your ability to perform some of the more aggressive actions like jumping, mantling, sprinting, and performing melee attacks. Naturally, juggernauts would be exempt from this (perhaps blast shield users too), but anyone else who survives a shotgun blast won't be able to run or dodge the follow-up shot (or weasel their way out of the situation with a panic knife). They'll have to stand their ground and fight back the conventional way. This is what's necessary to let shotguns have a purpose in life.
One final note, heavier weapon types like the LMGs and sniper rifles could stand a new proficiency to let them have the 'crippling' ability too.