Your problem is not uncommon. Basically, the shad gets hit so hard that the hook is pulled through, and when you set the hook, the hook buries in the shad, instead of the hyb. I have solved that problem in two different ways.
First, on smaller 2-4" shad, you can cut small (1/16") inch pieces of 1/8" wide rubber bands, and run the piece onto the hook before you put the bait on. Place the band where the bend in the hook starts to straighten into the shank. That will prevent the shad from sliding on the hook, thus keep the hook from turning back into the shad.
Second, on the larger baits, you can run the hook from the corner of the baits mouth, and out the top of the nose, through the nose hole. On the smaller baits, there is not enough "meat" to keep the hook from wallowing out.
Now, where did you say that hybrid lake is located????