I understand that minor races don't have influence effects as major races do. But I don't think that they should be able to control mines from accross the galaxy with no fear of revolt. I think if it existed an unseen influence radius around them so they could control mines nearby but, not spaning the galaxy.
End of quote
That's the problem. Give a minor race space miners, and they will take lots of asteroid fields "out of circulation" as they colonize it for mines for the minor that can't ever be flipped.
They could be destroyed though, and I suspect that if Minors could use Miners (that sounds like something out of Galaxy Quest)...then lots of players (and possibly the AI) would be very prone to destroying their mines as the first step in a war.