I’m jealous of you, though. I have a thing for moths. Have you ever seen their cocoons? If so, how did they feel? The material feel like it was going to be easy to work with, or no?
Sorry to say, my only encounters with any member of Lepidoptera is limited to gardening, and usually ends in a squish. Only I may eat my cabbages, no invertebrates allowed.
Which Greek moths? That's my problem. Is it all of them including Saturnia pyri? I also imagine there's a little bit of variation between populations in terms of cocoon quality. But, I think you're right. My POD is 5,500 years ago, and in that time I should be able to justify the butterflies of an alternate Indo-European migration making their way out to Iberia with enough time to come up with a finer silk through selective breeding ("Say! This is a really nice cocoon! It's so soft! And look at those fibers. We're not boiling this one. Nope! This one gets to breed!").
Actually, at this POD, you probably wouldn't need to change much. Large moths were common all across Europe and Noth Africa. Also, breeding for a silk production bug boi would be surprisingly easy, bees had already enjoyed a lot of breeding experiments by this point, and that was for far more nebulous qualities, such as behaviour and selectiveness in nectar collection, but they went extraordinarily well, considering the limited amount of scientific knowledge available to breeders.