My story is exactly the same as the OP's. As I understand it, when the fine turns into a bounty it only affects the jurisdiction the bounty was issued under, so my assumption is that all I'd have to do is avoid this particular system after a week has passed. I currently have about 5.5 million in fines over this one thing, but it doesn't seem to matter in the slightest. The police scan me openly speeding out of the dock with half a kilotonne of illegal human slaves in my huge interstellar spaceship every ten minutes, and they just nod, increase my fine amount by a few million and let me continue about my massively criminal business in the assumption I'll be back in 7 days to collect my punishment.
I expect this is the same reason the station's market sells slaves despite them being illegal there. The slave vendors can rack up trillions of credits in fines for possession of hundreds of thousands of illegal goods every day, but as long as they pack up their shop and leave 10 minutes before the fines turn into a bounty, there's no drawback whatsoever to running a massive black market in full view of everyone in a system a stone's throw from the Imperial capital.