The Potential Meaning of John 1:14 (SARX)

I believe in soteriological redemption through the ransom sacrifice of Jesus Christ; John 3:16 is near and dear to my heart. Yet the idea that John 1:14 teaches that Christ assumed "human nature" is evidently an abstraction taken from the Gospel account. Maybe the abstraction is correct as Wallace argues in GGBB, but the Greek of 1:14 could easily mean "The Word became a human" rather than "The Word assumed human nature." (See BDAG under the entry for "SARX.") In other words, it's possible to understand SARX in a count noun sense at 1:14 as opposed to interpreting the signifier with a mass noun sense.