I have not had a problem with the plastic anchors when I have had to use them. It is better to have blocking behind the fiberglass or if you had a stud back there you could use 3" screws.
I have not heard of drilling into the pan to secure the glass framing and I am curious what brand you have that advises this. It is hard to set neo angle walls and keep them from leaking. It is very important to have the pan level and preferably square with the walls.