I've been messing around with small ponds for over 30 years and thought I would offer my unsolicited opinion and how I manage these bream.
Where I live any sunfish is called a Bream.

I have had remarkable success putting mature red ears into small ponds (under 2 acres) that only contained bluegill and bass. 3 years after stocking the big redears I began to catch some redear/blugill hybrids. These are realy beatiful fish and I've caught several that go over the 1 lb mark. The only drawback is the hybrids have become dominate and the bluegill population has fallen off. Now each year I add some mature bluegills to the mix to keep the bass happy.

As for greensunfish we built a 1/2 acre pond on a running creek. After it filled it was full of greenfish that came from the creek. I was going to do the standard bass/ bluegill stocking but didn't really want those greenfish eating my expensive minnows. Solution was to stock 75 channel cats. The catfish didn't realy clean out the greenfish but did help keep them in check. Next step was to move 15 2lb bass from our other pond. Now this was the ticket cause the bass grew like crazy and the greenfish population really began to go down. I was afraid the bass were going to run out of food so I began moving some bluegills in. Now 4 years after the pond was finished The catfish are about 5 lbs. The bass are around 4 lbs and I catch very few small bass.
And the bluegill and green sunfish have crossed and now I have homegrown "Georgia Giants" hybrids. In conclusion if you have too many greensunfish put is some predators and take advantage of the free food.