I was playing around a kind of similar idea at some point, where the fantasy was to shoot six times in a turn with a single shot shotgun.
https://underrail.info/build/?HgUFCwkKAwPCoEEAAAAAZAAyAAB9wocWCnMAAADCoAAAcjliKzHCsMKWJsKHwpgZRx3ChcKQwojCscKlwqbisaAF4rOsBeK3sAXfvwHonestly, I never really liked the way it turned out. Yeah there is a huge overkill with pellets critting and everything getting shred to bits, but stat wise it was tedious to build.
I would probably recommend not going over 6 agi with shotty, and regardless of not always wanting to benefit from leading shot, it is still worth it when you need to bump up the odds. So that puts pressure on getting 5 dex.
On paper the ideas are fun, but in practice, I never really found much use for Blitz and Hit and Run.
Crit is good for shotguns though. Crit and stacking Per is probably the way to go. Travel light, and tactically use sprint and ptc and it is all good...yeah.
Cannot recommend burst fire with shotguns. Different story if personal rules allow unlimited carry weight. Then it might actually be kinda fun
*edit
Now all that gave me a really dumb idea, for ironman run, and I am not even thinking it through, but what if:
10(18)/5/6/10/3/3/3 -> versa synergized shotty bursting tin can. Hmmmm... could carry those 4000 shells, easily
*
oh wait, would need Int of 5
Well, it could be a sledge/shotty hybrid
But, anyway, something like maybe 10(18)/3/6/10/3/3/5, or 8(16)/5/6/10/3/3/5