From what I have seen, minor races will not flip from influence. I am assuming that this is due to the fact that the computer tends to 'cheat' the minor races stats. I see alot of minor race planets that should be running so far in the red on their economies from the sheer number of factories on their home planets, but which still manage to pump out ships in one turn etc etc, and they always seem to have near (if not 100%) approval/morale. Which might explain why it is extremely difficult, if not impossible, to flip them. This may be why in most war situations, despite the fact that their ships are being destroyed and their whole military outclassed, they will only sue for peace and never surrender outright.
As far as influence bases go, what has worked for me so far is to put the influence starbases either just inside my influence zone, or if I am trying to influence a smaller area (i.e. a lone colony or another starbase) I put the influence bases on the far side of the enemy area, so as to squeeze from two fronts. I have yet to see this piss off another major race, which leads me to assume that, while a physical strabase presence might be inflammatory, my influence area expanding into theirs isnt considered overly aggressive.