Oops. I guess I mis-stated the problem. This is an example of what I meant when I said that radio waves to the brain would explain a lot. I can still retire to a farm, but I get confused sometimes. Might milk the chickens instead of the cows.
When I tried recording with Mic as the only source, I didn't get any DC offset! Then I realized I hadn't actually tried that since discovering the DC offset problem (since I had a hard time finding the microphone). So I played with the control panel and tried other sources, just to compare, and I found I couldn't get the DC offset with any source!!!
After much experimentation, I now think this is the correct statement of the problem: Whenever Stereo Mixer is selected as the recording source, and
Phone playback volume is not muted, a large DC voltage is introduced into the recording signal, which is added to any sound that's also going into the stereo mixer -- i.e., the problem only occurs when Phone is one of the sound sources. Same on all machines.

- AudScrShot2.jpg (30.07 KiB) Viewed 860 times
I guess it must be that Phone wasn't muted before, and I didn't notice it because I didn't have it selected to appear on the volume control panel. And I guess in my previous experiments I was always using Stereo Mixer as the record source, and isolating the actual sound source in the mixer panel. Doh!
I don't know why Phone wasn't muted. Maybe the result of some other experiment, a long time ago, now forgotten (with the radio-fried brain problem, that could mean last month). But with Phone muted, everything works the way it should. If I ever want to use a phone with a computer, maybe I'll have to study this again and find out why it happens. But for now, problem solved! Thanks for the nudge that sent me onto the right track.