I spun a copper dome when I was at teachers training college 45 years ago. I wanted to make a mould to form expanded polystyrene domes in. As mentioned above I used a very tough lathe even more solid than my graduate . As I remember It had a live centre to press the metal onto my pattern which I turned from beech. I threaded my pattern blank so it screwed onto the thread of the spindle and turned it to shape on the same lathe. As I remember there was a pretty strong post in the saddle that I pivoted the spreading tool against. The tool was basically a steel bar that the end had been rounded and fitted into a blooming big handle which I think I had to tuck under my arm to hold it steady. You mention annealing the copper, I had to do this quite frequently and quench it in the acid bath. I only made one incompleat dome from copper as it was really tough going. The tutor suggested I try aluminium as it was much softer, which I did. The ally had to be frequently annealed as well, which was a bit of a game taking the piece off the lathe and centreing accurately when it was replaced. I made a larger hemispherical dome 250mm diameter with a 50mm rim, then turned the pattern down by 10mm or so and turned the inner part of my mould. All the time I was doing this the tutors and technicians stood well back and told stories of when they were in arircraft factories in the war making the noses of planes and the disks coming loose, flying across the factory and out through the wall.
I made my polystyrene domes, cut them with a hot wire and then cast the pieces to make an aluminium 3D jigsaw puzzle. I still have my mould and the pattern somewhere but the college kept the jig saw puzzle in a display case as nobody had ever done anything like it there before and the college had supplied all the materials. Those were the carefree reckless days and time seemed to run much slower or days were longer!