I took the ST546 apart.. and ahha! Blown electrolytic caps inside on the PSU circuitry. So I've replaced those now, and we'll see what happens with it again over the next day.
The modem now works as good as new -- equal to the st516v6 I had replaced it with. On our primary line, it
(as well as the other two modems) is solid.
So today I put the
known-excellent st516v6 modem onto the suspect line. And the same wanky line condition struck at about the same time again this morning (10:42am).
So, I think the three modems are all just fine (now).
And one of our two lines has an issue of some sort.
I'll ignore it for now, and deal with it in the New Year.
Cheers