A few updates:
I glued the center pole on my first prototype (eliminating the shock cord and the two cord stoppers on that bar)

Here you can see where the cord stoppers used to be.
I also looked at the chair’s feet, they could be removed entirely, but it would expose the poles to a new type of damage (especially in carbon) but they could also be trimmed. Each foot weighs 6g, but cutting them shorter can save about 2g each (this is an 8g savings across all 4 legs

original

After a trim

Back on the chair
Together so far I’ve dropped a bit more weight as you can see here:

12.77 oz
By way of experimentation:
I cut up an REI chair fabric today, I removed the pole cups to see how much of the total weight is in these reinforced sections vs the rest. Here is what I found:
Total weight: 80g
Pole cups: 35.1g
Main fabric:Â 44.9g
I think that main fabric could be replaced, but I think best case scenario it could reduce the overall weight by <1 oz (22 g). The fabric cost on something like this would be more than the cost of an entire replacement fabric from REI, so it’s probably not worth it beyond a passion project, but still fun to work on.

Here you can see the pole cups are about 1/2 the total weight of the fabric on the chair.