Thanks for taking the time to type in such a comprehensive answer. I think I can respond to nearly everything in it.
The "silver wire" is likely a shield drain wire. Does the pickup have 4 insulated wires plus the "silver wire" inside a larger insulation that covers all 5 conductors? That is standard stuff. I have a FRED from the mid 90s and that's how it's wired I have some much older 'buckers from the 80s and they are the same way.There is no "larger insulation"; that's one reason why I was contemplating adding a spiral shield to the wires coming from the pup. In fact, I can't even see the white and black wires that Dimarzio's sheet says are permanently soldered together; they must be under the pickup itself. All I can see are green, red and silver wires, which are wrapped around each other on the way to the control cavity. BTW, this pickup is probably about 15 years old. I bought it new and I don't believe I ever did anything to it out of the ordinary. I also never used this guitar that much, and certainly not with a high gain amp where I was trying to keep the volume control turned down a good deal of the time. In retrospect, I think this beast (it is a great, raw sounding Tele) has always been played with the volume on either 10 or 0.

But now I want to use the volume control with this more responsive amp.
The ground wire from the bridge, the silver wire, the green wire and the SLEEVE of the output jack should all converge on the back of the volume pot. The fully counter clockwise terminal on the volume pot should also be grounded to the back of the pot. One side of the TONE Cap should be soldered to the back of the tone pot and the back of the tone pot should have a wire running to the back of the volume pot. The other side of the tone cap should be attached to the center lug of the tone pot. The fully CCW lug of the tone pot should be connected to the fully clockwise lug of the Vol pot. The pickup RED wire should be connected to the fully CW lug of the volume pot. The center lug of the volume pot should be connected to the TIP of the output jack. That is IT. There is nothing else that needs to be done here.Everything is just as you describe it, with this exception: the tone control cap is grounded to the back of the volume pot instead of the tone pot. There is no wire from the back of the tone pot to the volume pot now, but there was one until yesterday when I removed it to see if it was necessary. Since there was no change, I left it off. Continuity readings with my meter show the tone pot's back to be grounded anyway, presumably through the metal control plate.
Make sure to use good quality pots. I prefer CTS. Some would say for your stacked 'bucker a 500K Vol would be better, but I think 250K is OK usually. Worse case you lose a little output level. Same with the tone. Worst case you lose a little top end by using a 250K. Wire it all very cleanly, and use a good quality iron and rosin core solder. Be sure to use a good known cable to the amp. Comparing to other guitars is OK I think since you have so many guitars. To me the symptoms sound like the volume control outer lug is not grounded.The pots are Alphas, 500k. The outer lug of the volume pot is grounded to the back of the volume pot, which is connected to the sleeve of the output jack and also the wire from the bridge.
The only other "odd" thing I notice is that the tone cap is an old chocolate drop style unit. (I've had this guitar since 1970 and I have no idea when that was put in, but it works fine, AFAIK.) Could a bad cap do this?
I am getting a little tired of the drain this thing is putting on my amp building activities (it has become a first class diversion) and I may just have to live with it if I don't come up with something. But then, that's what I always say...before I tear something apart again, LOL.
Thanks again for the detailed response.