Uhh, so wow. Empire kind of sucks for trading. There's no high supply to high demand routes that anyone has found. Also, the faction rep gain was broken. Um....not so much anymore.
I did a cargo run in my viper (shut up, it's upgraded to 8) and found an Imperial Navy quest to find combat stabalisers. That shit is prohibited in empire space. I would have ignored it except for the Imp Navy thing. Hmm..maybe that's how I finally gain rep. I have been doing everything I can think of and I still am neutral with the Empire. I had to run waaaaay outside to find an anarchy system that sold them (combat stabalisers). It was around twelve jumps. My viper gets around 10.2 ly jump distance (I knew splooging my money on the A frameshift drive would work out).
Anyway, returned the goods and, now I'm an OUTSIDER to the empire! Woot! I'm no longer neutral!
So, if you're an empire person, if you see a mission marked IMPERIAL NAVY something or other...the reward for that is a direct upgrade in status for the empire.
Apparently, you get the missions from Empire Dictatorships...though a few reports have come in from a few stations not sharing that description.