"The one-wire continuity problem was one I had faced in the past, when I was helping a friend fixing up a very old two-story house."
Two story, one wire, but I ahve three stories. Does that mean I have two wires? Actually, I have 12 Ethernet lines with eight wires each. To locate and document the connections, I used a DMM after making a test cable that shorted the two middle wires together. Then I just had to run around with the sorting cable to each Ethernet jack and listen for hte beep in the wiring closer where all Ehternet lines come out of the wall.
Those DMMs with audible continuity testers will sound when the resistance measured is below some threshhold, but not always that close to zero ohms. In same cases, you get the beep but the resistance is still too high for things to work.