I haven't really analyzed every little piece of this, so bear with me on it.
The Idea
What I propose is the shotgun bursts get affected by the fast shot trait or reduce the AP of the shotgun by 1 in burst mode in general, and reintroduce the spread effect of the shells, but at the same time boost the general damage output by 30-50%, or give them the ability to cause a stun effect (3 seconds of immobility, or something along the lines of that, or even a temporary reduction in the targets ability to-hit-cap by 30%), alternatively add armour penetration to them instead.
General Banter (not important, just reminiscing...)
Because at the moment the shotguns are completely useless in my opinion, as were they before the wipe, the only good time I had with using the shotguns was when the AI was so flawed that it ignored you if it didn't have you in it's LOS (good times, clearing caves with a 10mm pistol, or a H&K CAWS agains ripper armed cannibals)