What the official instructions don’t tell you is that you also need a Torx screwdriver to complete the task. These are for the odd little six-pointed star shaped screws used to attach the drive caddy (or mount, whatever it’s called) to the drive. You have to take the old caddy off and attach it to the new drive.
I can only guess that they’ve omitted this as perhaps the official Apple replacement drives come with the caddy already. Whatever. Torx screwdrivers are sufficiently exotic that I didn’t have a set. Luckily for me there was still a branch of Trickies open within the greater urban area… so a quick 40km round trip drive later I had a new set of screwdrivers and the new disk in.
This was really my fault for not reviewing more of people’s experiences in doing this. Then I would have known.
Further reading on MacBook hard drive replacement: