Make solid from swept surface (face mask)

[Anonymous]

I'm having a hard time creating swept shapes in Fusion 360, especially going from surfaces to solids.

The goal is to thicken the attached surface to 2mm (to the outside, preferably). 

I keep getting errors that suggest "modifying my geometry," but without specifics, I'm not sure how to proceed. Any suggestions or resources would be greatly appreciated. If there are other workflows for achieving similar shapes, I'm very open to suggestions.

[jeff_strater]

the areas of high curvature are going to make Thicken fail:

Those likely will cause the offset surface to self-intersect, which will cause the failure...

[TrippyLighting]

My model in this thread demonstrates another technique.