LB:
My thoughts on reducing GC numbers (which I think are roughly in tune to the general consensus) is that you can reduce them by 1 or 2 a year, with a concentrated but not herculean effort. Since I foresee you want 1 , maybe 2, 3 at most GC; such a small reduction would be significant in your pond.
GC can be caught on hook and line (I have hooked GC on mealworms 7 or 8 times this year, managing to land 1), bow-fished, or taken with firearms (I had 2 of them 2 feet from me, eating pellets next to the dock I was laying on). But their learned caution would, I believe, make it hard to take more than one (every year or so) by any of these methods (they have not taken a mealworm as bait since I caught the one).
I did not mean it was easy to reduce GC numbers - there are several folks who have too many and are struggling to cut the numbers. But in a small pond, getting 1 or 2 out should probably be all the reduction you'd ever need.