17 Draconis is broken currently and Sothis/Ceos seem to dry up with data missions. I have however found a way that allows you to rank up quite quickly.
Its best if you use a Conda or something with considerable cargo space. Buy some Clothes, Fabrics/Leather, Animal Meat, Algae, Grain and head to a system currently in a Famine State. Mode switch like a boss and only hand in the goods in your cargo for amounts less than 16/20. You get the same increase whether its 1 or 1000 items. You can also do the donation missions. I did find that some famine missions only grant you 0.1% in some cases which I found frustrating, but the donation missions were doing 0.3% - 1.0% per mission when I was Post Captain.
I did my Ensign - Lt. Commander rank in a week by various things and I thought I would never get my Corvette. But in 7 hours yesterday, I got from Lt. Commander to Rear Admiral doing what I just described. I must add though, I did do a considerable amount of charity missions and probably blew close to 70 million. I got the food and other goods to lower the amount I donate and it seemed to work considering that a few nights ago I blew close to 100 million in 17 Draconis for 2 ranks before the system broke or was fixed.
Can't remember the exact names, but head to Russell Gateway - Cupinook, buy famine goods, head to son Dock - LR Hydrae if its still in Famine and mode switch like a champ. Remember that the mission boards refresh once every 4/5 minutes, so watch some YouTube, play a level of Candy Crush, make a brew or roll a smoke in between. If you have a dual-monitor setup, watch some Netflix during the grind. It will take a while to get used to the mode switches, but it pays off in the end. Especially if you join private groups too as these sometimes connect you to new transaction servers. I can get 5 different mission boards on a good day, 2 on a bad day with Open, 3 Privates and Solo.