... what is the bullet proof way to ensure the cherished phone number is not lost and how to switch the FTTC service with the absolute minimum of down time to the new provider?
Given that the existing incoming landline cable to the house will already have at least two pairs of phone wires, your family member could order from the new ISP a new additional SOGEA installation - that would involve fitting a second master socket to the existing cable using a spare copper pair, without the need for a new cable being installed.
Once the new ISP's VDSL service was up and running, there would be almost zero downtime switching their broadband from the old BT service to the new ISP, and would avoid the slight chance hazard of the street cabinet not having any spare connections.
They could then port their BT phone number to their chosen VoIP provider, and in doing so ceasing the BT broadband in the process.
When I ported my phone number to VoIP, the downtime of having a working phone was about 30 minutes.
The disadvantages of this approach is that they might have to pay the new ISP's installation costs, and you end up with two master sockets on the wall, however it would be the belt and braces (almost "bullet proof" way) to ensure the "cherished phone number" is kept AND with minimum downtime.
Just make sure that the new ISP and the Openreach installer are clear that you need an additional (i.e. second) connection, and it is NOT a takeover of the existing line.