The original problem came from using a Lightning adapter on an old 30-pin docking station/radio as the phone would not rest against the docking stand. This seems to have distorted the connector and as a result, the charger cable would make an unreliable connection to the phone.
The guide is excellent, but especially the first time was a long slog. Prying loose the screen, finding all the relevant screws, dealing with the standoff screws (little !@#$%^&...) and knowing when to pull on what bit. Alas, a few more times of opening it all up were needed. It turned out, after another couple of taking everything out and putting it back, that the microphone on the replacement part was faulty: though Siri would hear me and the speaker phone would also work, but regular phone calls were impossible. Thanks to iFixit for a speedy shipment of a new replacement part, I've just closed the phone up for (hopefully) the last time! But if I were to have to open it up again, at least now I can manage the unscrewing and re-screwing in about 45 minutes.
1) Stick to the guide!
2) Keep your screws in order: a magnetic mat is likely best, but drawing boxes on a piece of paper for each step and type of screw also does the trick (though having a curious cat around is a riskier factor).