If you watch the way the priest gives the blessing, and you follow his hand motion, you would actually be doing it from right to left. Over the centuries, the good people in the pews began to imitate the priest (left to right, just like he gives the blessing.) That stuck as the norm for the Latin Rite. Eastern Catholics and Orthodox still make the Sign of the Cross right to left.
So, technically the Eastern Church does it the more ancient way. Is it acceptable to do it that way if you attend an Eastern Liturgy? Sure. Is there any reason to do it on at your parish because it’s older? I don’t think so (believe me, you’d stand out).
In Christ through Mary,
Frank