I've used blendshapes many times and have always been able to solve this one, but something is wrong here and I can't figure it out.
The problem is that regardless of whether I set the "origin" option to "Local" or "World", the blendshape node incorporates the location information into the blend - in other words, the shape moves to the original position of the target.
I always understood that setting the origin option to "local" overcame that, but not this time.
FYI - both surfaces are extrudes - I created one, then duplicated the generation and path curves, altered them and re-extruded. Both surfaces have been altered on a component level after the extrusion and after history was deleted. The surfaces have identical topologies, surface direction, etc.
I also tried re-ordering the deformers, but there aren't really any to reorder - just the blendshape and the tweak.