Screw/revolve/spin tweaking?

I’d like to put a sharp edge where I drew a red line, and also, the other side has inverted faces.

But this model is made from a profile and just the screw modifier, and I’d like to keep in that way (non-destructive, etc. etc. But I don’t know how to flip a face and mark a sharp from just a profile consisting of edges and vertices. Can anyone assist?

screw.blend (903.6 KB)

it’s a 2.8 file

yes it is…