It should be possible. I've done some spinning a long time ago. I don't remember ever trying to do anything with quite that small of throat though.
What I think I would do would be to make my mold then start out with a small sacrificial disk say 3" in diameter see how it turned out You can always make a small funnel out of it later. Then go to a larger disk say 4" take note of how much further up the mold the disk wound up and go from there by the time you are ready to make the actual part you will have a fair understanding of how to do it.
On thing don't try to achieve the final shape in only a single push up the mold. Work a small short distance up the mold from the throat then run your spoon across the face all the way to the outer rim each time you push a litter further up the mold the metal needs to be allowed to flow fluidly as you work it into the final shape taking care not to try and take too large of a push at a time to prevent the edged from wobbling fiercely. Be mindful that you are forcing the metal to stretch and shrink at the same time. Once you have your completed shape simply part off the excess .