I found a supplier for wire mesh and attached it over the face cage of a hockey helmet with zip ties. The supplier is a company called Belleville. Their website is
www.bwire.com . You can buy one foot squares, or larger chunks to your dimensions. Unfortunately there is a $50 minimum order for the larger pieces and a hockey face cage requires a 14-15" X 8-9" piece, so the 12" square won't work.
If I remember right, I got .032 or .035 wire diameter with a .123 spacing, galvanized to lock the wires in place. Even with a cage underneath to support the stucture I wouldn't go any smaller on the wire diam. as a matter of fact i suggest stepping it up to about a .04 unless you go with a smaller spacing than I did. Any exposed edges need to be wrapped somehow or they will shred sparring weapons.
good luck with figuring out how to attach it to your helm. Hope the wire mesh info helps.