Your whole arguement hinges on them being cousins, not brothers. The Bible obviously does distinguish different levels of family. If they were really Cousins instead of Brothers, I think that the Bible would have spelt that out. It does elsewhere.
First of all, the argument does not "hinge" on them being cousins. The claim is merely that they were not biological children of Mary. One possibility, which seems consistent with the text, is that they were cousins.
It's really beyond dispute that neither Hebrew nor Aramaic have specific terms for cousin or nephew or brother in-law or half-brother That is why Philip the Tetrarch is identified as Herod's "brother" in Scripture, though he was really Herod's half-brother, and why Abraham addresses Lot as "my brother," though the text elsewhere makes it clear that Lot was really his nephew.