If you're willing to drive a bit, you could go to the Rend Lake Spillway. There are lotsbigheads in there.
Horseshoe lake in Alexander County has lots of asian carp in it and they rent out boats.
That lake is near Olive Branch, IL.
(it's much closer than Rend)
Also, you may want to go to
www.Siloutdoors.com and ask this question there.
Good luck!