Perfect method for outer profile of a grouped artwork

I made this effect in illustrator today (the one on the right). The shadowy rectangles are jpegs renders and the linework is pure vector pasted above the jpeg. However, I used the paint bucket tool for this composition to get the outer profile to make it thick then did the effect.

However, if I draw some rectangles in illustrator, do a grouping, apply a new stroke in the appearance panel, drag it down the contents name, I get the effect. This however wasn't happening in the first image scenario where I have lots of blocks, the new stroke applied to the group was getting applied to all the lines and not the outer profile which is my requirement. The lines of the cuboids and cubes are all strokes, simple strokes without any fill.

In the rectangular composition creation, I also met two conditions, one with contents option visible, a

and one without.

I want the outer profile method to work every time. What should I do?

While making the outer lines as thick, I do a grouping