I can SEE the lower part of the screw through the hole in the stem and I'm
sure the water is leaking from this hole (probably squeezing past the
screw threads). WITHOUT the screw, the water squirts from the hole under
pressure. Caught me by surprise, it did.

This hole that leaks......are you saying it is the same hole as
the screw screws into, or are you saying that it is a hole that goes
through the side of the stem?