Greeks: E + G2a + J1 + J2 + T = 58%
Most J2 (23%) must be J2b, more likely Southeast Mediterranean. A core of the rest is what makes Greeks 32% Mideast/Cucasus, with a residual 0.5% Northwest African. There is 41% of other haplogroups that probably replaced African autosomes and reduced others.
E1b1b falls under Mediterranean, otherwise nothing makes sense in the comparison between Dodecad admixtures and Y-DNA frequencies. J1 probably should be divided in J1c3 and JxJ1c3, but overall J1 and T are better classified as Southwest Asian.
For the Greeks, G2a + J2 = 29.5%, much closer to the 26% West Asian admixture. You can't expect a perfect match because these are rough averages. J1 + T = 7.5%, a very good match to the 6.8% Southwest Asian.