Swept boss/base: need profile to be orthogonal throughout a helical path

Hello all,

I am trying to sweep a diamond-shaped profile in a helical path along a hemisphere. I want the profile to remain such that the diagonals are orthogonal and parallel to the base of the hemisphere throughout (i.e. vertical and horizontal). Illustrated below:

Running the sweep with the above profile along this conformal helical path yields this geometry:

Any suggestions are much appreciated.

Thanks!

SolidworksModeling And Assemblies