I'm
guessing that you may be facing an unforeseen problem. It is possible that when you bounty hunt in an independent system, even if you find a small Fed outpost, that bounty hunting only increases rep with the system
controlling faction, rather than just the base you turn it in at. I have made over 35 million in bounties, and I'm not even sure on this one.
Evidence A:

This is all from Bounty hunting (Except the Alliance, that was from the Community goal to expand/explore.)
If that turns out to be the case, then I have a solution for you.
Disclaimer: I take no responsibility for this being a completely stupid idea that does not work, even if performed flawlessly. Try at your own risk.
Run up a huuuge Fed bounty claim in the independent system (like 2-5 million) and "smuggle" them to a nearby Fed system
(I hope you know what I mean). The only real danger is being interdicted otw to the station, but I know how to fix that.
A: SOLO mode. At least when you "go for" the smuggle run. Last thing you want is a griefer ruining your big shot.
B: When interdicted. . .SUBMIT. I
cannot stress this enough. You know when you get interdicted,
and 80% of the problem is that you have to wait for the Friendship drive to charge, so you can run?
well, submitting actually solves that problem. Instead of a 30 second FSD "cooldown", you are granted the 6 second cooldown for submitting.
Then, ZOOOOOM! gone. No NPC can kill you in 7 seconds, I promise.
C: Smuggle your bounties into the station (maybe check the bulletin board for even better ways to raise rep.) The problem with using BH to gain rep, is that your killing Fed pilots also, so it's more of a give/take, rather than a take/take. Successful missions grant take/take rep rewards. AND! Exploring, that is also a take/take rep method! Go exploring for a week, smuggle THAT info to the feds, and not only will you get a significant rep boost without risking death, but you'll make a cool 4-10 million on the side!
Using this method, you should be able to climb the ladder back to unfriendly. While your correct that you can no longer hunt in Fed space safely, you CAN still reap the rewards of turning those bounties in. Unless it works just fine turning them in to a minor Fed faction in a non fed system. Then this a lot of work for no gain. But sitting here typing it, I'm not gonna lie, it sounds FUN!
Hope this helps!
ps:Once you are at unfriendly, pick a fed system to call home, and BH there. Identify the controlling fed faction, and let those ships go ( I know, I SAY it easily. But the odds of me not shooting up a python worth 130k bounty, just because he belongs to _____, are pretty slim, because I'm pretty greedy. But if I was SMART, and backed into a corner, this is exactly what I would do. About 2 hours before returning to these forums to cuss out the guy who talked me into it.