Hi,
I’m not saying there is never a good reason to mix up the deformation order, in order to achieve specific outcomes. However the standard deformation order, serves the most common use cases, say facial blend shapes and body corrective blend shapes, where you would generally not want the blend shapes to be evaluated after the skinning.
In the classic setup, blend shapes are either authored relative to the bind pose or authored relative to a skinned pose, where the skinning is then subtracted before the blend shape is stored (to effectively make it like the blend shape was authored relative to the bind pose). At runtime blend shapes and skinning are then applied in order on top of the bind pose.
Judging by the video you originally posed, a similar solution should be possible to re-create using the standard deformation order, given the appropriate authoring pipeline is implemented.
In a perfect world, Unity’s OOTB deformation order would be user configurable, but it is currently hard coded to the industry standard, which mirrors what I’ve seen in other engines (I pretty sure Unreal uses the same deformation order). If that does not work for you, your best options is to extend/replace the deformation pipeline using compute shaders, which from experience is totally doable.