It would be misleading to say that the "dominant ethnic element among Eastern European Jews is Judean."Based on the MtDNA (mitochondrial) evidence, you could also say, "the dominant ethnic element among Jews is European."Because the vast majority of MtDNA (the female DNA) is European in origin - haplogroups H and K.And about 1/3 of the male chromosomes (Y DNA) is European or Eurasian based.Combined, this means that Ashkenazim today are at least 50% European in ancestry.I believe this is accurate.
Now, the majority (70%) of Y chromosome results from Jews indicates "Judean" ancestry - primarly haplogroups J (J1 & J2) and E, though J2's history among Jewish populations may be much more complex than you are crediting it.So that makes about 35-40% of Jewish ancestry attributable to Middle Eastern (mostly Northern Levantine) origins.
I don't think haplogroups R1a1 can be directly attributed to Khazarian ancestry, though it can't be ruled out either.My father, an Ashkenazi Levite, it R1a1.About 52% of Ashkenazi Levites are R1a1, and 12% of Ashkenazim overall fall into this haplogroup.We can't really determine at this point if it came through Khazarian or Slavic ancestry.The irony, of course, is the that fierce R1a1 Kurgans who are the founders of this haplogroup are considered the epitiomy fo Indo-Europeanism.The homeland of the Indo-Europeans is the steppes north of the Black Sea, right where the Khazarian Empire was located.But the problem is that not only were Khazars most likely significantly R1a in their ancestry, but most Eastern Europeans are also R1a.So we can't really tell the difference at this point.The two populations are interchangeable.
However, the same cannot be said for haplogroup Q among Ashkenazim, which is considered by researcher Doron Behar to constitute a minor founding lineage among Jewish populations.Approximately 5-10% of Askenazi Jews today are in this haplogroup and it originated in Central Asia.It is an extremely rare haplogroup in both Europe and the Middle East, found only Scandinavia and the few countries that Khazars were known to have migrated to - Poland, Hungary and Lithuania.In fact, Kevin, you have argued beautifully in your own research (which I have enjoyed reading) about the movement of the Khazars to these particular countries, as supported by archaeology evidence.It is also supported by linguistic evidence as well, particularly in Poland where places and streets are named for the Khazars.But the group of people from Europe with the highest percentages of haplogroup Q?Ashkenazi Jews.
This is not to negate the ancient Israelite origin that some of the DNA evidence indicates. This is significant and a wonderful confirmation of our connection to the ancient Israelites. But rather it shows the complexity and richness of Jewish ancestry.Looking at Jewish ancestry as purely "Judean" in origin is both limiting, inaccurate, and not appreciative of the full picture of our ancestry.