Well, I couldn't get enough heat from a soldering iron into the gear wheel from my soldering iron. It's only a 50W iron, and even cranked up to full, the heatsink of the brass gear was too great to stop it getting any hotter than uncomfortably warm.
So it was out with the Dremel, and the careful use of the slitting disc... I had to make a series of cuts to first of all get the gearbox out, then to extract the gear wheel itself. There wasn't enough room to cut it immediately in the middle and slide the axles out.
This picture shows the four parts that the axle wound up in!
From here, it was easy to use a gear puller to get the gear off the axle. It was then cleaned up, and re-mounted on an axle stolen from my other Pug kit. I must get some spares from Alan Gibson when I next see him at a show...