I dont have a hard time getting pinch harmonics at all. on any pickup. my 1077XL has ToneZone 7, and as much as i dont like that pickup, i can get harmonics off it. Pickups play an important role, but if you arent getting them at all, you might want to take a look at what you're doing.
Read this:
http://insaneguitar.com/col/joel/Joel37.html
That should help you refine your technique a bit.