As part of the research in the Binkley Name Study, we find one of the Binkley's married a Johann Leonhard Moser (aka Leonard Moser), born in 1710.
According to the Biography on his profile:
Leonhard immigrated to Pennsylvania aboard the ship Adventure in 1732.  Also in the Adventure were his full brother Tobias, full sisters Magdalena and Christina, half-brothers Georg Philipp and Johann Michael, various spouses, and many younger Moser dependents. His full brother Johann Adam and half-brother Johann Martin had previously immigrated in 1728 aboard the ship James Goodwill. Johann Leonhard’s half-brothers were all sons of Adam Moser by his first wife Maria Strobel (1652-1696).
Note the name of Johann Martin Moser that I bolded above, his half-brother who emigrated earlier.
It also just happens that Johann Leonhard Moser's ancestral line also traces back to Switzerland, as you can see on his profile.
Johann Leonhard Moser eventually made his way down to North Carolina, and I'm descended from him.
I would hazard a guess that this is the same Johann Martin Moser that you are referring to. If so, he's not the only Moser immigrant, or progenitor in America.
Take a look at this Moser line as well and see if it helps.