Hey bassman,
I also struggle with noise. You have run a good set of tests. The fact that the noise reduces when you turn the volume on your guitar down means that it is not coming through the power line. This is also confirmed by your battery/ups test. So any noise conditioners you purchase will not solve your problem. Since it's not coming through the line, it must be coming in through the air. As others have said, good shielding and grounding will help, as will eliminating the offending transmitters.
I spent a summer at my father in laws house outside the city a few years back, and my guitar playing never sounded better. When I returned home, I suddenly realized how much noise I live with in my home. When neighbors turn on appliances (especially motors) I hear them as noise, and since it is RF, its nearly impossible to block or eliminate. So I have taken great pains to make sure my cables and guitars are all really well shielded and grounded, but it is still a small problem.
One thing I will add is that the newest noiseless single coil pickups (I have some Dimarzio Areas) are better at removing hum than almost all humbuckers. Also, if you do like hummies, get ones with balanced coils (same number of winds on each coil) for maximum hum canceling. I don't know how actives stack up in this regard since I don't have any. Anyway, good luck.