Thanks for the help everyone! I can't get the pickup to push down at all, so I think I'm going to have to take it all apart and carefully notch the pickguard at the neck. The store where I purchased it from offered a free setup, so I figured why not? Well now I know: the bridge pickup was so high the low E string would hit it when picked hard, and the neck pickup is either as low as it goes, or the screws are jammed.
I think I learned my lesson.