Sentence Correction

What is wrong with A?
Thx
For protection from the summer sun, the Mojave lived in open-sided, flat-topped dwellings known as shades, each a roof of poles and arrowweed supported by posts set in a rectangle.

A. each a roof of poles and arrowweed
B. each a roof of poles and arrowweed that are being
C. with each being a roof of poles and arrowweed
D. with roofs of poles and arrowweed to be
E. with roofs of poles and arrowweed that are

For protection from the summer sun, the Mojave lived in open-sided, flat-topped dwellings known as shades, each a roof of poles and arrowweed supported by posts set in a rectangle.

A. each a roof of poles and arrowweed
B. each a roof of poles and arrowweed that are being
C. with each being a roof of poles and arrowweed
D. with roofs of poles and arrowweed to be
E. with roofs of poles and arrowweed that are

I think A is absurd/changes the meaning..a dwelling can't be a roof and that is what a intends to say...but at first look, it's very difficult to neglect A
Is E the OA?

Good point. E is right. Thx

IMO - A

E is wrong due to subject verb agreement
arrowweed that "are" does not agree with the Mojave "lived"

IMO E is correct because these structure are still known as shades. The part after comma just describes its attributes.
Well, i couldn't find any subject-verb agreement error here..

https://www.beatthegmat.com/roof-t13278.html

googled it

Hmmm, but we still don't have the OA..

'A' might give an impression that the arrowweed alone is being supported by the posts.

We need the 'are' in 'E' to imply that the arrowweed as well as the roof is supported by the posts.