Thanks, and that would probably be really helpful, if I had any idea what you meant by "run rebuild on your arc'd curve".

I can't find a Rebuild command or any way to do anything similar other than drawing the curve over again from scratch for the 50th time.
How does one do this?

Also, I don't really Want to Stretch the cone.
When the cap is placed on the bent ice-cream cone, I want its total height to be 50mm, but I cannot come up with any way other than pure trial and error to get the heights to match so the open top is merely tilted, not displaced vertically.