Reputation can be gained (and lost) on a ward by ward basis. When you help the ward and its inhabitants you get rep, and when you hurt them you lose it (GM discretion). [...] The inspiration here is the faction rules from Blades, but shifted to focus on wards rather than specific factions. IDK if it will end up being what I want, but this is where I'm going to start.
Merely an observation, but something that is overlooked with the factions in BitD is that the citizenry of each district are their own factions too, so your ward idea is essentially the same in practice.
Probably a 1-5 track for the positive side.
If reputation can be lost as well as gained, presumably it can be negative as well as positive, in which case I'd suggest a +3 to -3 scale. It seems to be the most intuitive.
Speaking of wards and BitD, one of the things I found genuinely underrated was the Traits section. While ostensibly intended for fortune rolls, it implied a lot about each district in terms of fiction at a glance. If we compare say, Brightstone and Barrowcleft:
Barrowcleft
Wealth: 1
Security & Safety: 3
Criminal Influence: 0
Occult: 0
Brightstone
Wealth: 4
Security & Safety: 4
Criminal Influence: 0
Occult: 2
Brightstone is a wealthy district filled with homes of the nobles, so of course it's wealthy, and power protects wealth so naturally it's safe and secure by extension, which in turn means no crime. All makes sense. But what about Occult? Well, it's where the main cathedral of the Church of Ecstasy is (and they engage in some freaky stuff behind closed doors) and the factions section tells us it's where the Circle of Flame is located.
Meanwhile, Barrowcleft has a low Wealth score, but a high Security & Safety. Why? It's where all the farms are, and that's the domain of the Ministry of Preservation. Lots of working class manual labour, hence the low wealth, but if anything happens to the food...well, "there are only nine meals between mankind and anarchy". Sure, many of the nobles have their own private electroplasmic grow houses and will be insulated, but if the citizens starve, they'll have do things themselves!
Quelle horreur! The farms have to be protected.
On top of that, most of the districts have their own special effect.
Granted, from what I've seen in the Blades community, the overwhelming majority don't utilise this section at all, so maybe it's not worth taking inspiration from, but I personally found it the best section of the district write-ups.