Is there any way to have the middle position on my Am.Std Tele three-way switch become this cocked wah sound?
Not that simply, no.
Which pickup(s) should be involved? If just one, yes, I think it can be done, I need to find my drawing.
If both pickups, then you can't do it with the three-way like that. You could add a mini-toggle or push-pull to kick the cocked wah on, no matter which pickup(s) are selected.
Or you can use a superswitch. That's a 5-way switch, so you could do:
Bridge
Bridge+Neck (parallel)
Neck
Bridge x Neck (series)
Cocked Wah
In any order...