I asked my AD, who'd never been asked to look into straps, so that may or may not work out, but there doesn't seem to be any ability on the Tudor website to order straps, or even contact them, for that matter. I have a BB 58 and BB GMT, both on the bracelet, but with summer coming would love the specific NATOs shown on the Tudor site. Any help would be appreciated - thanks!
When I wanted a strap for one of my own Tudor watches, I called a local retailer and showed them the link/picture of the strap that I wanted. They said they would look into it and if needed, they could order it for me. It later turned out that they had an extra one laying around that I could just go in store to pick up. Link to find retailer: https://www.tudorwatch.com/retailers/unitedstates#near&place=ChIJCzYy5IS16lQRQrfeQ5K5Oxw
I ordered an OEM NATO for a Tudor BB from an AD without any problem at all. I'd go back to yours and be more insistent.
Are those 20 or 21 mm? I tried to buy one last year and ended up not doing so because it was the latter. Most if not all of my watches are 20 mm.
Not OEM obviously but I picked up a few of the crown and buckle Chevron straps. They are a pretty good substitute
The 58s are 20mm, GMTs 22mm. Data for each model can be found here: https://watchbase.com/tudor/black-bay
The Crown&Buckle Chevron straps are a really nice substitute. Similar to the OEM straps, they allow you to adjust the length so you don't have to do that double fold, which I really hate. They also look really nice to boot!
Any rsc should have a stock of straps and bracelets if there is one near you. I London I got a bracelet and nato for the Tudor gmt (when I owned it).