Simon has provided some sensible good advice.
It took 3 attempts before I got mine with pickups sitting at the right height. The long J Bass Pickup Mounting screws sounds simplest but there are deep holes on either side where the PUP's are normally mounted on those plastic rings however the part with no thread near the head will be a problem as that will require that hole to be drilled out and then no longer able to be used with a thread.
I hand shaped some maple headstock off cuts to fill the holes so they were flush with base of PUP rout and glued them in place and then drilled separate holes in the PUP mounting lugs and used wood screws with high density foam underneath base of PUP's to provide some way of keeping them level and provide a bit of spring action for setting the height.
There may be photos on my build diary but here are a selection of close-ups that might help to illustrate what was done...
If I was to do this again on another build I would use a strip of metal which is similar in width & thickness as the PUP lugs, drill same sized mounting screw hole so that driving the mounting adjustment screw would create a thread, and screw this mounting plate separately to the bottom of PUP rout cavity. You could use the spring but it still needs the high density foam to prevent PUP sitting at an odd angle.
Hope you get some inspiration and ideas from all of this.
Cheers, Waz