Thanks to Kappy for offering suggestions. No, quitting Contacts doesn't help, because I rarely use the app anyway; and neither does a reboot. This thing acts like a fast growing cancer, taking over your CPU and preventing you from using any apps.
But rather than wait for other replies I tried Linc Davis' 2013 solution, and it worked.
Linc's description is quite detailed and conservative (to keep you from screwing up), but you'll find it under this thread...
How to stop AddressBookSourceSync
I took some shortcuts. If you use iCloud, un-click Contacts from the list of apps you sync with iCloud.
The general idea is to get rid of your AddressBook (it's still called that in your system library). Apple doesn't want you tampering with that stuff, so you need to know how to get there. Copy "~/Library/Application Support/" (without the quotes of course) and go to the Finder. Click Go▹Go to Folder, then paste the folder address you just copied. That gets you in.
You'll see AddressBook in the list of Application Support items. Drag it out to the desktop. You'll only need it again, if this solution fails for you, and you need to restore it by dragging it back where it came from.
My AddressBook had so many hundreds of duplicates of contacts (likely created by AddressBookSourceSync itself... maybe that's what it was doing while burning up my CPU), that I didn't care if I ever saw it again. I could get a copy from one of my other Macs if necessary.
That was all it took for me. Linc warns that you may have to restore (import) your contacts from another file if Contacts opens empty. In my case it opened fine with my complete list... and WITHOUT the thousands of duplicates that had been spontaneously created. AddressBookSourceSync still exists in my Activity Monitor list, but now consumes 16MB instead of 16GB. I'm a happy camper again.
If you're worried about losing anything (especially your contact info), PLEASE use Linc Davis' detailed instructions via the link above. Better safe than sorry. I was simply too frustrated with the problem to give a ****, so I cut corners.
I'll update this if the problem recurs, but I suspect that this case is closed for me.
BTW Linc Davis has solved so many problems for me over the years, that no one else could touch. This guy should get an Apple Medal of Honour or a huge annual cash award for what he's contributed here.