We ended up building relationship maps and only using the setting’s baked in factions as jumping off points. Sure, there are the BLUE COATS, but you have to deal with Sergeant Prescott and the 19th Precinct.
We also started going around the table after generating the score and letting every player add an embellishment to the score that might tie into their character. The mark is a former MILITARY man who wears your regimental tie. The client is a SKOVLANDER too. The score is happening in a warehouse that also contains something you need for your long term project. Explicitly tying in backgrounds and cultures and goals at the beginning of the score helped us hit our character marks.