If the "Davidic descent" notion seems more plausible, there is good reason :)
I have been slowly working backwards from al-Andalus and the Maghrib back through Palestine into Babylon....then back to Palestine. I am in the midst of sorting out the pre-talmudic academies and 'resh metlita' thereof. Adding Talmidic references and extant sources...as well as biographical info where possible. In essence reconstructing Shalshelet haQaballah of the Babylonian Tradition, and clearly noting where the Palestinian tradition diverges.
At the moment the Exilarch branches are correct from 2nd Temple period forward. Three (2) lines are incomplete
1. Shealtiel of Catalonia whose origin is sone of last Gaon of Pumbeditha. I've already started to fill-in the period between 999 and 1099. The original Catalonian lineages were provided by Moshe Shealtiel-Gracian; providing the bridge between Catalonia and Hachmei Provence back to Babylon.
2. Dayyan of Aleppo whose origin is Babylonian Yeshiva of Eretz Israel; Yeshiva was moved to present-day Damascus and Aleppo. Mitch Dayyan has been very helpful so this will go quickly - especially since his Family authored a text "Sefer Yashir Moshe" which is a family-specific version of "Seder Olam Zuta".
3. Abravanel of al-Andalus whose origins can be traced to Nehardea - Shmuel of Nehardea's Academy. This is a more difficult line to work with since there are gaps...but not material gaps. It seems to parallel another lineage which will clear itself up in little while.
I have finished the Charlap lineage through Mar Zutra II back to Exilarchs of Palestine who fled to Babylon...all those famlies which decent from "ibn Yahya Family of Spain and Portugal" have clean path back.
I am trying to sort out Abravanel, too, but in order to do that I MUST get my head around the pre-Talmudic and post-Temple destruction academies, Resh Metlita and Gonim. Abravanel Lines trace back to "Rab" then branches into a different lineage (from Zutra and Bustenai lines) that appears to have been in al-Andalus before 2nd Temple destruction. I'll get this straightened out in another 30 days.
I've recently been side-tracked with Yosef of Fustat and his descendants - there is a peculiar confluence of families in Lucca and Rome which circumstantially appear to connect to Jews of Troyes but that's gonna take a lot of digging to sort out and that will take until end of 2013.
However, please temper your "Davidic descent" claims. There have been times where different lineages inter-married which confused lineages; daughters of the Daividc lines married non-Davidic lineages and these new non-Davidic Lineages then adopt the claim...and this has gone on long enough that more than a few families will be very upset if they are not genealogically connected to David haMelekh through paternal descent. Paternal decent from David haMelekh is a complex son-of-a-gun and it'll take some time to build out the profiles with concomitant sources and biographies.
The DNA analysis proves this complexity - there have been adoptions of Kohen orphans by Davidic Families, 2nd son exchanges with non-Jewish monarchies, and a host of other reasons that the DNA is an incoherent mess. To net it out, there are two sides to the descent formula and the female role in this cannot be trivialized...or overstated.
Hope that helps.
J