"Hello, Shady & Shady solicitors. Yes sir, we're a neutral and independent provider. Sorry sir, you want me to contact whom? Can I ask why? Oh, you've incurred an accidental bounty and are unable to return there to pay them 600CR for fear of having your ship blown up by local security? Certainly sir, I can have that amount wired over to them and I'm sure that will then right any moral wrongs you have incurred. Yes sir, it would be nice if you could contact them under amnesty, but then our out-of-the-way outpost is a handy stopping spot with a lovely view of, well, other stars. You're welcome sir. Call again soon."
Having had a similar thing happen to me, I share the OPs sentiment on this issue. It seems to me that this new system is targeted predominantly as preventative action against high volume player killing sprees, but incidentally inflicting unnecessary pain on low severity infractions.
I think something more in keeping with the universe FDev has created would be better. How could it work? Well, for starters there is no "interpol" in space. You have local systems (with a controlling minor faction), and across these you have the three main factions to which they are aligned (or independent).
Minor faction fines span the minor-faction controlled space only [ I'm thinking collisions / speeding etc.]. Your fine follows you in major-faction aligned space, but it is just a fine.
Non-controlling minor factions can only issue bounties - no attacks from local security: pirates and bounty hunters only. If you attack one via a mission you're only wanted by that faction (because they're small, and not protected by the major faction).
Outer-space infringements from combat cross all space aligned with the major factions and are "Wanted" bounties. Likewise, attacking a base owned by the aligned minor-faction.
Outside of these conditions, nothing carries over so if you do generate a local fine it doesn't become a galactic ball and chain. If you've been naughty in federal space, well go to the empire (after all, why should they care?). And yes, you can leave fines behind in independent space because after all, there're no galactic space police - just various factions looking out for themselves. If you want to risk going to independent/anarchy systems, you're game. If you stick to faction controlled systems, then you'll have the security there to help protect you.
PS All aligned systems should have an ability to pay off a fine.
On the 'big one' - i.e. PvP murder: the key 'penalty' in this game should be time. Money currently is the only penalty, and that doesn't scale. For a new player just ganked, that rebuy could equate to ten hours play. For the perpetrator, the bounty could equate to five minutes. A percentage of assets then on capture? Or an impound on the ship for a time period? In court normally fines scale so that mega-rich footballers pay a proportional fine or a community service time so that it isn't trivial. Voluntary impoundment of a ship by docking at an amnesty system to clear your time; or hunted in jurisdiction space otherwise?
Sure, this isn't fully fleshed but you've got to allow criminal activity to be carried out without making it a pain for the little folk. And more importantly for me I think, it's a galaxy in conflict so many factions would be more than happy to see some turmoil in an adjacent system.