James,
Welcome to the forum. It always seems to me that there ought to be a Byzantine presence in the area, since there are both Greek and Antiochian Orthodox parishes there and, where the Antiochians are, we Melkites usually are. I have a vague recollection that there was a short-lived effort at establishing a Melkite mission there, some years back, but that it was not successful. No one else has any presence in the area and from my recollection of Texan geography (which likely hasn't changed since I was there 40 years ago), Alburquerque may be closer to El Paso than the few EC parishes and missions elsewhere in the state.
Many years,
Neil