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.