Hi David, I am investigating the same issue. I have family ancestors with given names like Moses, Aaron, and Mordechai, usually in alternating pairs (e.g., several generations of father-son named Moses/Aaron/Moses/Aaron), and three generations of Mordechai's. Of course, a Christian could certainly bear these names from the Hebrew Bible, it just seems more indicative of some sort of Jewish identity.
Their last names included Mendenhall, Schoemaker/Schumacher, Cooke, Ellis, and others. Ostensibly, they were Quakers. Some of the ancestors (e.g., surnamed Cassel) came at the behest of William Penn to escape religious persecution in continental Europe in the mid-seventeenth century. I have at least one document that claims that one of the families (surname Op den Graeff, related to the Schumacher's) who came from Holland "were Spanish or Portuguese Jews" escaping the Inquisition. My theory is that some of members of these family were crypto-Jews, and they found refuge in the Quaker community, which did not require statements of faith. They settled in the backwoods of North Carolina, Pennsylvania, and eventually, Ohio, with my most recent branch settling in Cincinnati, before coming West. In the 1930s, when my great-grandmother married my great-grandfather (heir to this Cincinnati family) if his family was Jewish (a strange question to ask at that time, no doubt), his mother replied, "We don't ever discuss that," or "Don't ever bring that up again."
But it's come down to me to indeed bring up this buried issue.
Did you ever test your DNA? DNA is not conclusive, but it can give you leads. I was not satisfied with 23&Me, FTDNA, or MyHeritage, but I would recommend DNA Consultants. They are a company out of Colorado, and they go a bit deeper, claiming to get at the autosomal DNA (whereas they claim the other companies only do mitochondrial or Y-DNA). It's also a bit steeper, but it will definitely show if you have markers for Jewish ancestry (I think they have like 7 different Jewish reference populations, as opposed to the other companies' 2 – Sephardic and Ashkenazic).
Let us know what you find! Feel free to reach me at joshuajohnson555 at gmail dot com