Hi, an update:

I tried the teflon thread sealant with the old brass valves
and the new PVC fittings. I also tried the tape and
"cleaning" the valves' threads with a steel pipe fitting. A
real tap, from a tap and die set, is not convenient. No
luck; the joints leaked. Plus, I suspected the PVC-valve
joints I was hoping to leave alone, some eight years old,
would soon start leaking. So I replaced the valves.

I bought PVC ball valves, 3/4-inch and 1.25 inch to replace
the old brass, gate valves. I actually throttle one of the
valves to adjust the flow at times, so ball valves are
better for this. Generally though the valves' positions are
fixed for months at a time. Large diameter PVC ball valves
are often difficult to operate and so test the strength of
connecting joints, so I remain apprehensive about how well
this will work in a few years. Just recording these thoughts
for the archives.

Since the PVC pipe proceeds into the ground just a few
inches beneath each valve, I wanted to cut and cement as
little as possible off these ends. What "saved" me is a PVC
fitting called a "male compression adapter." It has male
threads on one end and a compression fitting at the other.
The 1.25 inch size adapter (mostly or entirely made by
Mueller B&K) was hard to come by, but I finally found a
couple of Ace Hardware stores that have them. Lowes and Home
Depot do not. I used teflon tape on the male threads.

All seems to be holding well; no leaks now. Plus the system
is quieter when the pump is on. Not sure why exactly that
is, but surely the joints were weak, or the metal of the old
valves loaned itself to facilitating air knock leakage
cavitation yada.

Lessons learned from reading and working with old and new
PVC fittings and brass valves: Partial replacement of old
PVC piping systems can grow into bigger jobs. Replace as
much as possible. I am sure cement joints are more reliable
and cheaper, but I wanted "forgiving" parts in this, one of
my first experiences re-piping with PVC. Also, I was trying
to avoid having to dig up PVC piping (about ten feet in
distance, maybe four feet deep, from pool filter system to
pool).

I am sure the experienced folks could have nailed this in a
few hours. I'm in it for the experience. :-)

Oren, noted that sealant may be better than tape in the
desert. I am in desert, too.

Thanks again all for sharing your insights.