On my A coupe I put the headliner in before the top. It let light inside the car. I put a liner between the wire and wood bows to prevent rattling from wind. Also marked the existing tack hole locations so I didn't have to drive thru metal.
I used something different. No nuts involved.If you put the headliner in first, it is then impossible to access and install the 8 screws and nuts (2 at each corner) of the molding after installing the top...at least that is how it is with my 4 dr...
Since we are dealing with support for visible roofing, what was the purpose for the original "chicken wire"? Engineering question.
It wasn't radio. That is a bogus purpose. It would only sorta,kinda, work as an antenna.
I suspect it was used to proved some sort of support for the roof between the wooden ribs.
IMHO.