Like Bass, Northern Pike seem to tolerate the hot summers in Illinois just fine. Seeing as how they are part of the Pickerel family, I figure the Northern could substitute in the event Pickerel are hard to locate at your local hatcheries. You won't need many and they're easy to order. Perhaps they'll just feed all year round (like Bass).
Northern Pike are eating machines and it won't take but 1 or 2 per acre (10 foot deep) to have an impact. They will definitely pursue the 10" bass, smaller Carp, Catfish etc.. before the few scrawny Panfish you're describing.
If the water clarity allows you to catch 4 bass a day, I'm presuming the Northern will be able to hunt and likely get more Bass than the fisherman.
I believe the key is to (inexpensively) create enough structure for your Panfish to be able to hide and thrive. You're real problem appears to be lack of Panfish due to lack of cover.
Once the Bass are reduced and cover introduced, Bluegills and Fatheads will improve everything. But, they'll need places to hide and spawn.
If your budget allows, a truck load or two of gravel to make spawning beds could go a long way toward reproduction of all your gamefish.
Cull your Bass, introduced artificial structures (pallets) for the Bluegills and Fatheads, to hide, and you'll be closer to achieving some balance.
You can either harvest the Northern or they'll die off, but they likely won't reproduce in the silty bottom.
