Have connecting geometry in box morph

After some help with creating a grid on my mesh, I was able to get closer to the results I wanted. However, I want to create a hollow mesh for 3D printing with a solid surface made from these tiles, which are quite separate from one another. Is there a way to make the bounding boxes scale the geometry to connect with the edges of the other bounding boxes?

Currently: 

Hoping to have something that connects the tiles:
Thanks so much!