I used EdgeSrf from the arcs, it preserves the control point structure and weights from the input curves. Unfortunately it doesn’t know what to do in the middle, so it makes a very flat curved surface - but all that needs adjusting at that point is the middle CV vertical location and weight (all the others are already set correctly).
I ended up doing that by eye to a reference arc in an orthographic view, the weight affects the flatness of the surface curve, so it’s adjust the weight, nudge the control point so the apex is correct, compare along the arc, adjust, nudge, compare, etc… in the end I think I reached the limits of the display accuracy.
I had tried simple sweep2 but it didn’t work originally (that was one of my first ideas) but now I tried it and it is working… 
It looks slightly better than my handmade one and a lot less effort…
–Mitch