Well, it's sorted!
Today, having a couple of spare hours, I got out my soldering iron and built a little thingy to go in the power lead. It delays the power to the SSD for 1 second at switch-on.
With that in circuit, the SSD shows every time at boot-up. I eventually got brave and migrated drive C from the hard drive to the SSD.
Wow! Aren't SSDs fast! Boot-up takes a few seconds rather than a few minutes, and most of that seems to be waking up the other hard drives.
So if your SSD doesn't accle, try connecting the power to it a few seconds after the PC starts. If that makes it work, build yourself one of these:
http://jillings.org.uk/ssd_delay.jpg