I would go with the thinner material. The original material stretches and swells with age. I have run across two curtain failures, 1 the curtain swelled and became too thick to wind to the smallest aperture ( dragged against the body opening for the top roller), and 1 where the curtain stretched and was ridding on the roller flanges causing excess drag. In both cases the curtain seemed flexible enough to be considered good.
Space is at a premium in the body openings for the rollers. The thinner material will give you more latitude and will probably be easier for the mechanism to handle.

I finally got around to cutting a new shutter cloth replacement, the thicker
fabric I found wasn't very flexible, and like 45PSS said it probably would
have been a tight fit, if any once all 6 ft of the cloth was rolled .

But i did have some rubberized Player Piano bellows fabric that seemed
to be a good match, the OEM was .010 thick the bellows fabric was .008
a hair thinner but it felt right, The Player Piano Company had a .010
fabric but it was tan rather than black.

My question now is about the metal whatchamacallits ( ribs ?) that frame
the aperture openings, I managed to get all them off the old shutter
by swabbing acetone on them which softened the old fabric enough
to let me carefully pry the long edge open enough to pull them off.
I wound up breaking one of the outer tangs on one of them and it
seems to be a very brittle copper or brass.
Were they glued on or crimped on ?

The whatchamacallits or aperture stays were most likely crimped on as that was the technology of the day. They might have been soldered.

As best as I can determine their purpose is the keep the curtain straight at the openings to give even exposure.

In http://graflex.org/helpboard/viewtopic.php?t=5624 it is reported that current adhesives work well for bonding the stays to the aperture openings. I would use contact cement.

Lacquer thinner will work to soften or remove coatings also.

I wasn't sure if they were crimped or crimped and glued, since the ones
I took off didn't seem to have any glue residue except for at the ends
where the tabs were bent back, even then I'm not positive that the
residue was glue. It's going to be fun to see if I can reuse them.

Working on a Thornton Pickard shutter definitely told me the stays were
to keep the shutter curtain flat, I think the TP shutters were the fore runners of the
Graflex/Graphic focal plane shutter, and in the one I'm in the process of
restoring without the aperture stays the shutter fabric buckles as it's
wound on the roller without them, the aperture is just a big hole in the curtain
with nothing but two strips to wind up on the roller, the lower part of the
hole tends to buckle and snags on the interior of the shutter.