To answer my own question, and to help other users, I found that the "1A Schottky Barrier Rectifiers" on that page, in particular a 1N5817
worked well. Trick was to cut the track after bugging the diode on.
Worked well until I got over-confident with the "brief" part below:
Briefly (and I mean just a brief touch) connect the wire from D10 to Vcc.
Cue smell of burning and a slighty dimmer backlight, no on/off control. I imagine the transistor went.
Oh well. You win some you lose some.......