1. It depends which calculator you're using, and whether you're ready to take the study into account.
In the original calculator, all of these populations have a very small amount of WHG, just above noise level (like Ashkenazim).
In the study (Greeks aside), they simply don't have this component, and this is replicated in the optimised version of the test for WA populations (which is why this optimised version makes sense):
2. This is basically what I am saying: If there really is European admixture, it must've come from a population with very low to non-existent WHG, which is probably what the Eastern Mediterranean looked like during the emergence of the Diaspora (prior to the Temple's destruction).
It makes sense because, as you said, Jews went through a philhellenic period, and many had Greek names when they came to Europe (just read about the Kalonymos family).
Here again, the sole flaw with this model is the low amount of IBD sharing with Greeks... Another problem which arises from this model is that uncovering the real amount of pre-exilic Judean ancestry becomes a pain in the @ss because we'll be splitting hairs (much of what makes up Mainland Greek ancestry emanated from the Levant at some point, and since the pre-islamic Levant probably was Cypriot-like the difference becomes narrow and can only be obvious if more resolution is brought in.).