I used to worry about this, and so I used to trap as manny as I could and remove them, I now realize that worrying and trapping was unnecessary.
I also have been trapping and removing as many GSF (and BH's) that I can, but have recently again quit as the size of the GSF have gotten smaller, indicating I have got a lot of the 4" target size out for the time being (till the small ones grow some more).
My attempt is to keep the GSF numbers in check till I start seeing BG in the trap regularly. I think to date the GSF have been eating all my BG and RES fry and not letting them get established. So I have been removing 3-4" GSF and adding 3-5" BG (caught out of my big pond). Probably add 20 BG for every hundred GSF I have removed. I figured will keep this up and eventually the BG would have to eventually overpower the GSF. Once I start seeing about half BG and half GSF in the minnow traps, I'll quit worrying about the GSF in the pond and just enjoy them for what they are.