I was wrong about this. I had powered up the Stomp successfully so I assumed it was working, as on previous occasions when it had insufficient power it went into a startup loop, flashing up the splash screen then shutting down and restarting. This time, it went all the way through and responded to button presses, and to HX Edit. However, I hadn't been putting a signal through it. When I did, although it kept showing on the screen and responding to HX Edit, it neither made a noise nor responded on the tuner. Switching to the standard power supply, it did work. I can't find my current sharing lead so I've ordered a 5.5/2.1 to 5.5/2.5 adaptor and I'll use a daisy chain lead to current share, and see if that encourages it into life.
Edit: just to emphasise that the Stomp is a massive current drain. Very few pedals will require that sort of power. Don't be discouraged from using this for a "normal" pedalboard.