Thanks very much for the responses.
The adapters I have will supply charging current at four different voltages from 5V to 20V. So I assume some of the data lines have to be connected to permit negotiation between the charger and the laptop.
Edit: But looking at the myfixguide page, it looks like that's essentially the same charger as mine, and there are only three lines connected. So apparently just one data line to negotiate PD.
Anyway, I think I've waited too long to try a cheap solution this time. So I've ordered a new adapter on Ebay for $20. Once that arrives, then I can take the old connector apart and see if the Aliexpress breakout could be used to repair it. If successful, I would have an extra adapter on hand in case one dies again. But I'm going to research the extension cable further. The time to install one of those is when the adapter is new, so any future connector problems can be solved by just replacing the extension cable, if I can find the right kind.
I know everybody loves powering through a type-C port, but I don't. I would rather have a traditional barrel connector, as God obviously intended.