In the first 30 seconds when you show where we are at, my chest doesn't move

It seems like you need the "base_def_in" to be parented to the "bottom squash" and then have the "bottom squash" parented to the "Base".

The "Top squash" will also be parented to the "Base".

If you get lost you can refer to the schematic I drew in the downloadable files ;)