The poster is looking to grow large flatheads. Blue catfish and flathead catfish are very different in many ways. Blue catfish will readily prey on shad in open water. Some fisherman actually target them via trolling. The original poster made no mention of being interested in growing large blue catfish.

Flatheads are ambush predators holding tight to cover and the bottom. Forage species that would be good for flatheads in my opinion would be sunfish species, bullheads, suckers and as the flatheads get larger, common carp. Flatheads rarely spawn in smaller lakes, thus you could closely control their numbers as it would be unlikely they would reproduce in a 13 acre lake. Gizzard shad do feed on the bottom and no doubt would be effective prey for flatheads, however I think the other mentioned species may be more effective.

Gullet studies on flatheads indicate gizzard shad do not make up a large percentage of their diets where they are found. The record flathead for VA came from the Occoquan Reservoir. I reservoir I have electroshocked numerous times while volunteering with the VDGIF. During the shockings, flatheads were shocked up. Gullets were checked, and although blueback herring and gizzard shad are very common in the lake, the flatheads were found to be mostly consuming sunfish, bullheads and carp.