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Bottega del Rame has a few 3mm pieces listed on Amazon, Duparquet has some, and Soy Turkiye has some. (I did find Soy Turkiye products on Amazon, but I'm not sure if the seller is associated with them or authorized to sell, and one of the things I find appealing about them is their warranty (lifetime, including retinning and shipping). I wouldn't want to buy them from an unauthorized reseller and lose that.)
I do get it about the cast iron handles, I like the look of them too. I'm still really undecided. It doesn't help that I've never actually seen most of the products I'm considering.