Hi,
I can recommend two corps that are working on null sec sov (diplomacy is slow, but moving) and have lots of opportunities for pvp. The corps work together, the only difference is one is tagged for faction warfare and one is not.
Here’s Ushra’Khan recruitment thread: T.R.I.A.D Recruiting [Null Sec] [Minmatar FactionWarfare] [Ushra’Khan]
And here’s Corp Awesome: New Corp: Corp Awesome Recruiting