I did not consider your rainfall situation either. removing all the green sunfish you catch is a good idea. I assume that since the green sunfish population is high that each fish is relativly small. you may consider crowding the pond with adult largemouth bass. As long as the bass you stock are large enough to eat the sunfish. Let the bass do your work for you, then when sunfish numbers are down, catch some of the bass out and consider stocking large bluegill. As long as your pond is a true 4 acres you should not have much trouble catching out enough bass and it would be more fun than catching small sunfish
I have had good sucess correcting overcrowded crappie populations with this menthod. of course its easy for me to come across a hundred or so bass 14-16 inches in length (shocking boat). Even if you cant get you hands on that many bass, it wont take many adult bass to start the ball rolling. 5 fish per acre will make a significant difference over the course of 2 years.
you may also consider hiring someone with a shocking boat. green sunfish are pretty easy to shock up, you could just keep out all the sunfish caught during the shocking survey.
just some thoughts
