No one has mentioned this, so I thought I would just bring it up even though it's probably not the case.
I borrowed a neighbor's goat once because my own doe had died, and I had no milk. She was an Alpine and a very nice goat. Well, her milk would take forever to go through the strainer. I could not imagine why. Then I tried to make cheese out of it, mozzarella as I recall, and it would not form up into cheese. That's strange, I thought... then I tested her for mastitis. She had a very low level of infection in her udder. So the whole time her milk would not go through, it's because it was getting very slightly clumpy from a very mild case of mastitis. I went to the vet and got her some Today, infused her udder for the recommended time, and Hey, Presto! Her milk suddenly went through the strainer like a breeze and the cheese curd made up into cheese.
Due to this experience, if a goat's milk will not go through the strainer like I think it should, I immediately suspect she has a very mild case of mastitis. Instead of changing my straining system, I infuse the udder with Today and next thing you know all is well. YMMV.