Before anything, freeze the base geo and delete history. make sure its at world space.
blend shapes things to note.
1.) Do not smooth the object before doing the blend shape
2.) Make sure to rename the blend shape geo before applying the blend shape deformer.
3.) Do not delete history on the geometry after the blend shape deformer is applied. But u can do it before.
4.) Do not rotate or scale the blend shapes geo on a object level and never freeze transformation.
5.) Do not delete faces or vertices from the blendshapes.
6.) Do not freeze transformations on blend shapes. You can freeze before the blendshapes are created, however once the target shapes are created, do not freeze transformations on the base or target shapes. If not the base will fly back to the origin when animating.
7.) When defining a blend shape, the base shape must be selected LAST.
