Why Was Miriam Punished So Harshly?
Right off the bat I think the writer gets the wrong wife. Moses’ wife at the time of the Exodus was of Midian, which were not Cushites.
As for the traditions, well,they also present a pretty glaring error as Moses’ family were from Levi, not Judah. Miriam would NOT have called her family Jews. She might have used either Israelites or Levites, or by Levi’s son ... but she wouldn’t have referenced Judah.
Didn’t read it, but I believe Chabad to be the definitive explanation.