The digitiser had become insensitive down the entire right edge, to a width of 15 mm. Sadly, that's where all the Settings slider switches sit, so no more turning on Mobile Data etc. Also, the glass had a single crack running across it. About time for a new phone... but no!
After viewing the how-to video AND stepping through the slide-show instructions, I ended up following mainly the slide-show. The glass had separated from the screen, and popping up the screen with the suction cup lifted only the glass, leaving the plastic frame in place, so I had to get creative with a small screwdriver to pop it out. After that, disassembly went smoothly. Re-assembly also went well. The most difficult bit was plugging in the LCD connector: I just couldn't get it to mate with the socket, but finally it went in and held. Once the screen was back on, the phone powered up and worked perfectly first time.
During disassembly, take the time to study the way each piece fits together before disconnecting and unscrewing. This can save you from some doubts later on, during re-assembly. A magnifying glass is a great tool to help with this.