Thank you for posting additional images , Monolith .
It kinda looks like some id on the cast metal ring , too indistinct for me to tell , though ... perhaps a rubbing (made with a pencil/crayon & paper) might bring out details & clues there ...
Only problem I'm having with the great images it that I (we?) need to know which direction is which -
The 'warp' direction , relative to your images , would be great/crucial to know .
Are any of the second series of photos from the surface of the griffins ( I'd like to see that area , as to the question about it being brocatelle or not ) .
The warp would be the long 'cords/threads/fibers/strings' running the length of the hammock .
(the other threads running across @ 90 degrees relative to the warp , are known as the 'weft')
Also , pics taken from the back of such fabrics (and including a plain old regular quarter coin , for scale)can tell a story too ... just another 'weaving fyi' , esp. if you intend to post your cool hammock on more forums/places .