As far as I can tell this is the most accurate (and cheapest) build available currently for shotguns though I could be wrong; please correct me if I am.
Mp153 with 750mm barrel, Rem-choke, and the FDE Eotech (Perhaps due to a bug?) buff accuracy the most. The most accurate slug is the 12/70 HP Slug Copper Sabot Premier, It doesn't do a lot of pen so I wouldn't recommend using this against PMCs.
Good luck out there!
EDIT:
This works comically well and using slugs still counts for the quest.
Source: https://www.reddit.com/r/EscapefromTarkov/comments/f7r4ha/spa_day_part_1/