I gave it a good amount of thought about this suggestion. Localized Relationships would help me answer the question of why I see independent smugglers flying into colonies with their transponders off and the patrols aren't tagging them.
And also, I have taken note of having personal relation gauges that seem to be left unused, especially when any gains on that bar after helping a fleet in distress or a station quartermaster have no impact and just disappears after leaving. Even turning in AI cores increases personal relations, so how it could be used is something to think over. That personal rep gauge could be used to represent localized system reputation based on which faction the player's actions are supporting.
It's something I've been half-thinking about, in the same context. Definitely no promises; there's a major piece of this that I'd like to see in action before deciding whether it "works" and/or is worth expanding on.
The UI stuff is indeed a major concern; this really goes hand-in-hand with the increased nuance - or, one might say, complexity. I guess it's the "if you're selling, it's a violin, if you're buying, it's a fiddle" thing 
I wonder if it could work if you were nominally hostile - i.e. same as now - but the patrols just didn't hassle you if the patrol commander or the local military commander were friendly. That wouldn't capture the "you're only *hostile* locally" case, which is more involved, though - it's more important to be warned of unexpected hostility via the UI than it is of unexpected non-hostility.
UI nuances, I could just suggest using the sector chart and coloring the colonized star system names based on the highest local faction relationship's color. The tooltip shows the star system detail, so could just add another section showing the faction the player has the highest local reputation. Instead of the -100/100 scale, it is 0/100, starting at 0 as neutral to 100 as cooperative or famous. As for the detailed local relationships, it would be better done in the star system info page, as a system rep tab to show each faction relation. Only factions (except Pirates) with a permanent location can accumulate local reputation. For practical reasons and easy on the dev work to be done, the
local factions in the system will only recognize the player's highest local faction rep, so being a local hero has it perks of getting away with smuggling or quietly raiding, since authorities may dismiss those activities as slanderous rumors. It does have a drawback if there are factions that are hostile to each other and have locations in the same system. Unless the player is a local hero to Independents or other non-hostile faction, it can give the opposing faction any reason to treat the player like a Pirate.
This also discourages frequently getting caught using the black market in the same system (Especially Naraka and the frequently cheap fuel prices), or stealthily raiding planets too frequently to the point the local patrols should be scanning for the one fleet that keeps blowing up their station and taking their goods. These actions would raise local reputation with Pirates, but not increase the faction reputation with Pirates, and being more Pirate-aligned means Pirate fleets are more likely to ignore you during their raid by talking to the comms (and chance of recognizing your local notoriety) while lawful patrols are more likely to scan more thoroughly and find contraband or suspicious cargo despite shielded cargo holds, or just outright engage if Pirate alignment is too high for being a serious local threat like actively attacking ships and ports.
Hunting pirate fleets in a faction-dominant system will raise local reputation to the faction owning the system, while helping a fleet under attack and succeeding raises local rep of the fleet's faction IF the faction has a colony or station in that system. If the local faction is high enough, local patrols are more likely to look the other way and pretend your illegal and suspicious cargo are just regular cargo and left be without reporting or destroying them, and takes more to raise black market suspicion for faction reputation hits, or reduce rep loss if said cargo is tagged. In a Pirate activity/raid event, reputation changes are greater to reflect increased attention to the star system.
To balance that out, the local relations can degrade over time on a per month basis. That way, the player fleet can stay away until the heat dies down before making another heavy dose of shady business.
This suggestion may be a few months old, but this thread has been nagging at my mind and should help by giving a more detailed concept I can suggest.
As an off topic side note, I tried out some mods and noted that people in comms become persistent, so the personal rep stays. That alone gave me ideas. I may have some understanding of Java, but it may not be enough for me to make a mod and demonstrate the concept personally (and call it Local Legends for a touch of humor).
