Just made a pot of fresh coffee. 'Ground the Colombian beans myself. Percolated. The aroma's fab. Looking forward to my own fix in a couple of minutes.
I suppose that getting the polarity correct starts with the BT technician when the phone service is first installed. There's a need to ensure that the B wire from the exchange/street cabinet is the one that carries the -45v (or thereabouts). The A wire should be around 0v. These are required to power any handset that's attached.
Beyond that, though, my understanding was that the TIA 568A/B specifications of some years ago allotted the two centre pins on an RJ45 jack socket for use by telephony equipment (phones) and that, specifically, the B wire from the road had to go to pin4 on that 8-pin socket, and the A wire to pin5. The wire and pin colour codes on the rear of the jack module were supposed to assist in this, the B wire being assigned blue and the A wire being assigned white/blue. But with BT adopting their own specially-keyed 4-pin telephone plug in the 1980s, those two centre pins were hardly ever used by anyone and instead in due course became the connection for a modem. (The use of a phone directly on an RJ45 jack socket would have been a rare occurrence anyway, other than via an adaptor).
Whilst one of the effects of a wrongly polarised phone connection would be that the 'loudspeaker' in the handset would be 'pulling' instead of 'pushing' and therefore causing the audio to sound weak, the design/audio quality of most landline phones these days means that the majority of phone users wouldn't be able to tell the difference. Some of us do still use older, higher-quality landline phones, though, where you can hear the difference.
But whether polarity matters for an ADSL/VDSL modem is a different question. Like you, I can recall reading somewhere some years ago that it was important to get the polarity right for modems, because some were said to be sensitive to it, causing stuttering of the browser connection and poor response to screen. But perhaps things have moved on and modems are now designed to handle the two-wire connection either way around? After all, it's a single, twisted-pair connection, and certainly at the modem end of that connection there must sit a bidirectional transmit/receive device.
I thought I'd definitely wired up my connection to the Internet perfectly, when I last re-did it some 4 or 5 years ago (using a Clarity filtered faceplate and a hard-wired extension to the modem, employing an RJ45 wallplate and Cat5e cable throughout), but now I'm not so sure. I don't particularly want to start messing around with it, as I'll lose connection and thereafter need to recover my sync speed again. I'm currently asking the manufacturer of my modem-router (Billion), but I've yet to receive any response.