To add to the conflicting advice, do the easy jobs first, while the material is parallel.
Make the blank, drill and tap the end, reverse in chuck and form the dome.
Then screw onto a threaded arbor, and use Jason’s suggestion of a hollow centre in the tailstock, to support the domed end while the taper is cut
If you make the threaded arbor, and then do not disturb it , the thread should be concentric.
If the taper is longer than the Top Slide travel, you will have to turn the taper between a centre in the headstock and offset the tailstock. The hollow centre will accommodate the offset, but lubricate it.
Howard