Charity has been nerfed to hell and back in the Empire for some reason, even though there are still a few decent Fed systems like Taribes.
As someone who just completed the rank grind to Duke a day or two ago, here's what I know:
Tamar and Aymifa still give some donations, but not nearly enough to be useful.
Aditi has a lot of Shadow delivery missions and courier missions you can grind rank on, and it's a little closer in than Fehu, and seems to have FAR less pirate and cop harassment than Fehu or Robigo. That is still a looooong grind though.
What worked for me was assaulting Metcalf Keep on Cubeo 3A, and picking up missions on all 3 other star ports on that moon. (And switching modes a lot to refresh the boards.)
Having said that, I think it still took me around 3 weeks of hitting it HARD on the weekends and for a few hours every night after work to go from Baron to Duke. As a bonus, I made over 300 million credits as most missions give you around 100,000-500,000 credits there. I didn't bother with the missions for killing sentries unless it was to kill 1-4 of them, or if I knew I had time for like 4 sorties on the 5-10 kill ones. Barely hit any of these sentry-killer missions that weren't empire-aligned. (Yes, do the other non-empire missions for money while you're there.)
Here is a decent video to show you how to do this:
https://www.youtube.com/watch?v=Ph4rBpYtE64I went with the same ship and build (since I had already ranked up to Rear Admiral with the feds, buying a gunship was no problem, and cost me about 30 million, fully outfitted to my liking, but hardly A-rated), and I really liked it. About the only thing I did differently than Vindicator Jones here, is that I used ALL the surface ports for missions, and cycled the board through open, Mobius, and Solo at each one to stack them.
Also, I made my assaults in Solo, because I found if another CMDR would wander in nearby after I'd already killed everything, the turrets would respawn WAY ahead of schedule, and blow up my helpless ship on the landing pad while I was trying to get back to it in my SRV. Without that strange early respawn, you have PLENTY of time to go about your business after killing everything.
This was actually a lot of fun to start, but ANYTHING is going to get old after about 3 weeks (3? I started on around the 20th of January. Whatever that works out to.)
I hope this helps!