Unfortunately for this theory, the bible contradicts it. Check Matt xxvii:37, which has the titulus placed above Jesus' head. This would be possible only on a true (latin) cross, not a tau cross.
A titulus, or small sign, stating the victims crime was usually carried at the front of the procession and later nailed to the cross above the head. This sign with its staff nailed to the top of the cross would have given it somewhat the characteristic form of the Latin cross.
Saundra, thank you for posting this, although I did not see it until today (Easter Monday). Very moving. It's easy for us to overlook the very real human pain that Our Lord suffered.