That would probably work too, but I gave this a try yesterday and now the whole thing works pretty much the way I intended it to:

If you want to increase the voltage spacing between the LEDs you can add an extra diode in series (as I've done with Q1).

I've revised the PCB layout a bit to accomodate the changes, and it now measures 100x25mm (4x1").  I'll post the artwork here if anyone is interested.