The percentage of Jews involved in the slave [trade] was very, very small. Because they were still hounded by the Inquisition and the beginning of the transatlantic slave trade started about the time of the Chelmnitzky massacres when European Jewry was decimated. So most Jews were in no position to raise the huge sums of money that the slave trade required i.e. capital to buy the slaves, boats, provisions etc. Also, the Jews of the Ottoman Empire were too busy going to the slave markets trying to redeem the Polish Jews who were sold by Chelmnitizky's henchmen to Arab slave traders. This stretched even a well-off Jewish community to the limits since redemption of captives is a great mitzvah.
If you want to read a novel about this period read Isaac Bashevis Singer's "The Slave." The idea that slaves who have Judaic traditions learned them from their owners does not strike me as explaining everything that happened. First, some North African Jews were sold when the Jewish community could not redeem them from pirates, warlords etc. Second, the consolidation of power by the Christian king in Ethiopia also coincided with the beginning of the transatlantic slave trade and those Jews who did not commit suicide by jumping off the high cliffs or convert to Christianity were captured and sold as slaves. My own feeling is that the "free blacks" of Surinam who escaped slavery and established their own independent communities, and who have many Jewish symbols may be of Ethiopian background. If you wish to read about this history it can be found in "Redemption Song" a history of the Ethiopian Jews. It's interesting that when Saudi Arabia outlawed de jure slavery in 1962, there continued to be trafficking in Jewish Ethiopian girls. It would not suprise me if descendents of these women retain a memory of their Jewish heritage.
You also mention that the word Jew is a Khazar innovation. The word Jew comes from the name Yehuda which was a large tribe. The "y" sound as in "yes" changes to a "J" as a result of linguistic drift. You will notice that many people whose first language is Spanish say "jes" instead of "yes" after a while this pronunciation becomes fixed.
Arthur Kostler's theory that Ashkenazi Jews are the descendents solely of the Khazars has been disproven by recent genetic studies. Jewishness is not a question of who came first, DNA etc. but following the framework of the Jewish belief system.