The system used currently involves making people stack baskets better.
You need to clarify what good and bad stacking are. I am presuming you mean they put too many or too few baskets in a stack.
If, on the other hand, they are not nesting the baskets neatly inside one another that makes a whole different problem.
You should also clarify what the minimum number of baskets that will be processed is, e.g. is it one?
The stacks are a maximum of 6' high, since each basket is 1" high that means there should be at most 72 baskets.
However presumably people sometimes sling a couple of extra ones on the stack.
The first step might be just to have a fixed bar under which the stack is pushed.
That means you know for sure a stack never has more than 72 baskets.
Next you could use the light curtain suggested by Chagrin.
Alternatively you might use a single beam to detect and count stacks and drop a moving bar onto the stack measuring how far it has to drop to count the baskets.
To handle the different basket types you have two big buttons, and two lights above the sensor area, colored the same as the two basket types. Pressing a button illuminates the light of that color. A light stays on till the other button is pressed. So the opperator pushes the button corresponding to the baskets being processed and presses the other button when he changes type. You could add further sensors to detect operator error pressing the buttons if need be.