Well - did it. Took me about 3hrs, however the bulk of the time was spent trying to solve problems right at the end of the process.
Firstly, when it comes to easing the handle forward and out of the GT - there's no discernible way of unclipping the connector rod on the passenger side from the handle mechanism. I wasted half an hour trying to work out how that could be done, and ended up working on the handle as it dangled from the hole in the bodywork.
Secondly though, and this was the absolute killer, when I got access to the handle and unscrewed the broken hinge piece from it - as I separated it from the handle I saw that the hinge itself is cast differently to the one I'd got hold of. So either the handle I bought was wrong (possible) or Alfa changed their parts at some point. It's only a subtle change, but basically the new hinge I was introducing is cast flat to screw directly into the handle metal. The old hinge was cast with a diagonal "chock" out of it, marrying with a plastic lump glued into the handle, and the screw going in diagonally.
A lot of swearing later, having found this out at the very end of completely pulling the door apart, I set about filing the plastic bump down so the new hinge could be screwed into it. It doesn't sit entirely flush to the car now, but it's near as dammit. Really p***ed off though, nothing's ever simple. Also must have damaged the handle mechanism somehow as the spring to pull the handle back in after you've pulled it seems not to work. Great.