I attached it to the edge of a work bench with a G-clamp - not quite a vice, but it held it firm for me. I also put a set of grips lightly around the other end of the shaft to stop it spinning. Then I hammered, hammered and hammered on the drill bit but it didn't budge at all.
I had a go at pressing too, but with the sort of force it was needing, it would need everything to be lined up perfectly straight and I didn't have that sort of equipment.
I didn't try heat - as you said it's a little delicate and I don't really fancy cooking my dizzy, as the car is my daily!
It is well and truly seized.
I've given up on it for today and put it back on the car now