PROBLEM SOLVED !
A bright fellow in the Edmonton Linux Users' Group suggested "Flaky UART" as the problem. So I moved the modem to my second machine, ran a new copy of Knoppix 3.3 (Feb), configured the modem, and it "just works"!
Funnily, the UART serves Win2k fine. Still. I'll swap it for curiosity's sake. It's on a Shuttle (!) AV61 board.
I think this newbie has learned a lesson worth sharing: "when at first you don't succeed, try, try again..... NOT !
I'm convinced that troubleshooting a problem is best done looking in the easy places for solutions first, and trying easy fixes first, before looking for obscure solutions and hammering, hammering away.
In an hour, I could have switched to my second (or someone else's) machine.....and saved myself a month of frustration.
chada