OK, once again, thanks to all. The answer I was looking for, and that several of you correctly pointed out, was: I was the problem.
Upon replacing the one ex-battery today, the technician verified, as many of you have properly identified, that my three house batteries are indeed flooded cell and not AGMs. My bad battery had apparently run low on liquid, and you know the restů My original jump to them being AGMs was the view I had through the side of the exploded battery of condition of the plates and the material between them - it looked like glass matting and never having seen the inside of one, wellů.
The technician load tested the remaining "good" batteries to find them fairly weak and suggested I don't insert a good one with the two weak ones (and definitely not an AGM with two flooded cells).
As the battery box
is in a very confined location (and I'm apparently no good at servicing them anyway) I opted for the AGMs. So, no food
for the kids
for the next several weeks but there are now three new batteries in place.
Just kidding about the kids