Sounds like you have it covered.  Seems like a simple lathe job if you ignore
that 20” dimension What does your lathe look like?

Seems simple enough to make a cardboard negative shape to hold up against the
curve as you develope it.  You could also make a carboard shape for the outside
and use a drawknife or big gouge to get close.

There is one at the Franklin Institute in Philly that is about 5 feet across
made of fiberglass and not very fair (is lumpy in other words). You put a coin
in a slot and drop it and the coin rolls on its edge all the way around and down
into the hole - a way to make donating fun for kids.

The math escapes me

Ed Minch