The Omega straps are made of Cordura, which is a brand name of woven nylon. It's not exactly the same as sailcloth, but does look similar from a distance. A lot of so-called "sailcloth" is probably Cordura.
I was on a similar journey to you a few months ago. I always liked the look of the Blancpain Fifty Fathoms sailcloth strap and wanted something similar on my Seamaster 300. I tried several examples, including those from Barton bands and WatchGecko. But they all had one major problem, IMO.
There is very little padding at the end that attaches to the watch. On a dress watch, this is ok. But it makes the strap look a little anemic on a dive watch (like your BB58). After spending ~$120 on different cheap straps and not getting what I wanted, I finally bought the Dark Side of the Moon Speedmaster strap. Notice how thick it is between the lugs. It almost fills the entire gap and at some angles looks like it is a fitted end. I think this type of strap would look better on your BB58 than the thinner ones you find online.
You might save yourself money just buying the Omega strap you are trying to emulate if you eventually get it. That TAG strap actually looks just as nice and would probably be cheaper.
Good hunting.
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