Been suggested before, but I can highly recommend going to a station that has been attacked by the thargoids and running the evacuation missions there. I took an anaconda, absolutely full of economy passenger bays (plus a size 4 shield) and just ran back and forth between the station and the rescue ship. Took me a day to go from Recruit to Rear Admiral.
2 tips.
1. Pick a station with lots of fed/imperial factions. The place I did it had 5, and I think if there were fewer than that I'd have had difficulty filling up.
2. The board refreshes every 10 minutes, on the 10 minutes (13:00, 13:10, 13:20 etc etc), but it takes 2 refreshes to get a full board. I found that I could do the first run, do the second after 1 refresh, but then I had to wait 20 minutes before I could do a 3rd and fill up. Since you can't board hop anymore this is a good chance to catch up on your reading
From an RP perspective, I also found it to be a fairly "realistic" grind. I can completely see my character spending a weekend just ferrying evacuees from a burning station.