I got back from the black, paid my 5100 Cr bounty on me and found a HAZ RES site 20Ly away. While at that site, I did it again, this time I went to an asteroid base nearby called Moore's Charm. I took the suggestion someone made in this thread, and I turned off the sound in the game, minimized it whilst sitting in the ship and let her run for 3 hours.
When I came back my notoriety had diminished so I could pay the second 5100 Cr bounty on my head and went back to the combat carnage. Something I noticed about the System Authorities at this HAZ RES site, they're not green on your HUD and they're yellow and don't help you either, I got into it with an Anaconda and 2 Federal Drop Ships that were in a wing and had to bug out. They stripped my shields and had me down to 22% on integrity, rather humbling.