Move the poles of a spherical spiral closer to each other without deformation?

I am attempting to move the poles of a thickened spherical spiral closer together while maintaining its spherical shape.

I have tried to use the shrinkwrap modifier. Then I used a bend modifier. This method works, but I cannot figure out how to add thickness to the curve after the deformation and shrinkwrap.

I cannot simply put a bend modifier on the spiral, because it deforms the spiral out of its original spherical shape.

I have attached photos highlighting the new pole locations of the spiral, so you can see what I am talking about.

Any suggestions would be greatly appreciated!