I would use a loose loft made from copies of the same curve. (see file)
To get the mirrored version to be smooth join like you want, the second profile in the loft needs to be a vertical copy of the base curve and the others are scaled copies.
You can also get a similar result with Rail Revolve (See file)
With the RailRevolve in order to get the smooth transition with the mirrored surface you will need to make sure the second control point of the profile curve (blue curve) is vertical to the first control point.