You are of course right, and I should have looked sooner.
Since the server is measuring it's own supply then I think that it was getting something like the 1V--2V drop it was claiming at ~5W. But I was indeed worried that I might have a higher-current loose connection upstream that could be a real hazard.
So I did the sensible thing... eventually.
(I have now tightened all the screw blocks with the exception of those at the other side of the house, outside, and a couple near one of the smaller batteries.)
Rgds
Damon
PS. I have an even worse confession, which is that the system may have survived because of signal grounding carrying some of the required current. Don't look at me like that, please...