Mystery solved. I know high-gains have a reputation for sometimes being a little noisy but not like this. The noise was as loud as the signal. I replaced the pickups and now all is well. There was nothing visibly wrong with the old pickups so I was baffled. Then I thought what if they were exposed to a strong magnetic field? I wracked my brain and then it hit me. My studio monitors. From a past experience I knew they give of a strong field. In fact the problem first occured when I was recording direct. I can't imagine another explanation.

Sorry for the near-duplicate posts. It didn't appear for several minutes so I stupidly wrote it again.

I forgot to mention. My monitors are self-powered. Four-hundred watts.

David I'm glad you have this problem solved, yes you did have a major problem if the noise was as loud as the signal. I know you were at wits end and had even taken this guitar to a tech and it had him baffled as well. I would have not suspected the pickups and not both! It will be interesting if someone can answer or has some insight into a possible strong magnetic field damaging your pickups.
You have done very well solving this problem, thanks for getting back with an update. Electric guitars are always in some proximity to speakers so it would be interesting to know if this is the real cause of your damaged pickups.

Don't wave the gtr and new pups in front of those studio speakers..... that could be a very costly way to prove your theory!

A little history. About 10 years ago I was at a mall and on a silly whim I bought a model solar system. It consisted of concentric metal rings each with a planet, that revolved around the sun via an electromagnet in the base. One day I was looking for a better place to display it and as I passed my recording setup the planets froze in place. When I pulled it back they began turning again. Moved forward, they stopped again. It was then that I realized my powered monitors gave off a powerful magnetic field. Fast-forward to about six months ago. I had forgotten about the solar system experience and I had the guitar plugged into the recording system about three feet from the monitors. That was when I first started hearing the noise. There's the answer. I'm not savvy enough to know if any loudpseaker emits a strong field but I doubt it. I'm sure it's the 400-watt amplifier contained in these monitors that is the culprit.

Both loudspeakers and mains transformers as used in many power amps have the potential to have magnetic fields surrounding them. However, especially with gear intended to be used near analog displays, these components are shielded to minimize the effect.

However, I have a hard time imagining a magnetic field that would damage your pickups; I don't think for a minute that this was the source of your problem. While a pickup itself may have been defective, I think in the course of the replacement, you solved the problem, perhaps entirely inadvertently. But whatever works!

But both pickups had the same malfunction and were fine when I first acquired the guitar.

Yeah, I'm equally as suspicious as JH (although much less qualified to make a diagnosis) - there's no way this was the first electric guitar (or even the first Rick) to be played in front of 400w self-powered monitors.

Yeah, I was looking at our standard setup, and there's about 7800 watts right up there on stage with us!

Maybe he was playing non-Rickenbacker guitars through the powered monitors, so it affected his Rickenbacker!