Problem traced and solved!   (I wish I'd gotten it fixed before Getaway, but I was afraid of turning the techs loose at $90/hour.)

My built-in mic and camera had to be replaced (possibly because a TSA agent had caused my backpack, containing my laptop in its padded case) to tumble off the conveyer onto the floor in the San Diego airport, but who knows?   The fan inside my laptop was also being erratic and sometimes making loud noises.    The fan's neurotic behavior may have been why I sometimes got static when recording and sometimes didn't (during the past 7 months). Anyway, in this case it seems to have been a hardware problem, not the fault of iMovie.