Use generic fallback in stacked backend for non core routines

The non-core routines that don't directly return or store a key
structure often fall back to the generic routines under the hood. This
means we can miss propagating a retrieved key up to the top level of the
stack. Avoid this by only calling the non-generic version for the top
layer, then falling back to the generics which will do the appropriate
store on fallback.