I was going to reply that you would probably be the best predator on GSF, but 4Corners already put up a good post on that.

In ponds with abundant GSF, I find them to be both aggressive AND easy to catch. That is a perfect combination for you to make a dent.

Do you have any kids, grandkids, local Boy Scouts that can help you fish? Most kids love catching tons of 5-6" GSF.

When you say you only catch 1-2 at a time is that on artificial lures or live bait?

In Kansas, my solution would be put 8-10 cedars trees with a cinder block around the pond in 3-5' deep water. Have kids fish with worms on a small hook under a bobber. The cedars act a "fish concentrators". I have had kids catch over 20 from a single tree (plus a few BG), and then we move on to the next tree for more.

Do you have any "fluffy" cover in the pond to concentrate the smaller fish? Do you have any heavier cover with open spaces in between? LMB need the latter as "ambush cover" to dine happily. They use up much less energy if they can just hide behind a tree trunk and then suck up a clueless panfish as it wanders past.

Good luck improving your fish populations. That should be an enjoyable problem to undertake!