Is there a way to win more than 700 reputation per battle? Without paying, of course.
Yes, there is. Your reward is based on ship multiplier and how well you did in comparison to your teammates. You didn’t beat them by a large amount, so you don’t get a huge reward. I think on the first and second wins I got something nuts like 4x the score of the next best on my team, so I got big bucks. Note that using ships of too low rank will seriously nerf your reputation reward, which is why the first is lower than the second despite winning a similar amounts of credits, because I spent some time in the Dwarf.
Try to use ships that are at most 1 or 2 ranks below your maximum for whatever faction you have a contract with. Beyond that, you will get ridiculously low reputation gains.
As for making more than 700 per battle, you should be making more than that once you reach tier 2, mostly late tier 2 (rank 6). At rank 9 I’m making over 2000 per battle.
I am currently using Anaconda-M and Kite 