Surely a NATO is also just going to add 3mm to an already thick watch?
A CNS ribbed NATO should do the trick they are much firmer, I have used them on my larger watches.
Easy enough to cut and seal the under section if you want it single pass.
https://cnswatchbands.com/collection...0aAtn6EALw_wcB
I’m sure my Omegas are 1.4mm and Aevig are 1.5mm https://aevig.com/shop/premium-nato/ so going to say 3mm once doubled under the watch head.