I think the question is easily solved when looking at the way the priest blesses the people. Afaik both Roman Catholic and Orthodox Christian priests bless from the left to the right, am I right? Now, I suppose that it's the same for the Oriental Orthodox, but I can't be sure. Anybody can provide a clarification for this?
Anyway, the fact that the Assyrians follow the same use of the Eastern Orthodox, and that the same practice of responding to the priest mirroring the gesture of the priest from right to the left was common also among the Roman Catholics up to the 12th century, a possibility is that the Oriental Orthodox under the Patriarchate of Alexandria were the first one not to "mirror" the priest, but to "imitate" him, so that they used to cross from left to right. The same practice progressively came to spread in Western Catholicism after the 1054 AD schism, so that Pope Innocent found it necessary to repeat and stregthen the original right-to-left Sign of the Cross. Of course his efforts came to be useless, and the practice of "repeating" the gesture of the priest was prevalent in the West as it was in the Oriental Churches.
My conclusion is that probably the Oriental Orthodox churches under the Patriarchate of Alexandria anticipated the process of changing the direction when they were still in communion with the other Orthodox Patriarchates, and that the prevalent practice was still to have priests blessing from left to right, and laypeople blessing from right to left. In substance, all of these variations are equally worthy, and none is superior to the other. A possible explanation for variety in the first four centuries might have been that the Sign of the Cross was originally performed by laypeople with one finger and over forehead, mouth and breast, so that no direction had been established by the Apostles; the practice of the larger Cross came to be used in imitation of the priests, probably around the 3rd century, and might have become widespread thanks to the territorial unity of the Church within the Empire. Who knows?
In Christ, Alex