Hi Chris,
I made something a little while ago that might help. If you want to download this template and check it out, feel free:
https://www.dropbox.com/s/256lm1hn28g2eq4/StudioHippo-RiggedBox-Template.zip?dl=0
I’ve set this up so that the contents of each box are masked when the boxes shift/resize, but you could probably parent the precomps’ scale values to the controllers as well so they squish/stretch like your example.
Anyway, hope it helps!
Cameron