One small addition to your plan could be to try and add a few more larger LMB, like 16"+ in length, while removing a lot of green sunfish by fishing, seining, or trapping.

A 13" LMB could eat a 5" green sunfish, maybe (??), but not enough of them to see a dent in the GSF population.


Excerpt from Robert Crais' "The Monkey's Raincoat:"
"She took another microscopic bite of her sandwich, then pushed it away. Maybe she absorbed nutrients from her surroundings."