As an Anglican and a Catholic, I was taught to use the two finger method you ascribe to the Old Believers. The two fingers together represented the union of Christ's divine and human natures in one person. The three fingers (thumb, pinky, and ring) clenched in unity represented the three persons of the Holy Trinity. I believe this is universal in the west among those who do not practice the ignorant whole hand method.
Again the Orthodox way is more correct because the other two lowered fingers of the Orthodox hand cross signing represent the dual nature.
It appears on the whole probable that the general introduction of our present larger cross (from brow to breast and from shoulder to shoulder) was an indirect result of the Monophysite controversy. The use of the thumb alone or the single forefinger, which so long as only a small cross was traced upon the forehead was almost inevitable, seems to have given way for symbolic reasons to the use of two fingers (the forefinger and middle finger, or thumb and forefinger) as typifying the two natures and two wills in Jesus Christ. But if two fingers were to be employed, the large cross, in which forehead, breast, etc. were merely touched, suggested itself as the only natural gesture. Indeed some large movement of the sort was required to make it perceptible that a man was using two fingers rather than one. At a somewhat later date, throughout the greater part of the East, three fingers, or rather the thumb and two fingers were displayed, while the ring and little finger were folded back upon the palm. These two were held to symbolize the two natures or wills in Christ, while the extended three denoted the three Persons of the Blessed Trinity. At the same time these fingers were so held as to indicate the common abbreviation I X C (Iesous Christos Soter), the forefinger representing the I, the middle finger crossed with the thumb standing for the X and the bent middle finger serving to suggest the C. In Armenia, however, the sign of the cross made with two fingers is still retained to the present day. Much of this symbolism passed to the West, though at a later date.
Aelfric (about 1000) probably had it in mind when he tells his hearers in one of his sermons: "A man may wave about wonderfully with his hands without creating any blessing unless he make the sign of the cross. But if he do the fiend will soon be frightened on account of the victorious token. With three fingers one must bless himself for the Holy Trinity" (Thorpe, "The Homilies of the Anglo-Saxon Church" I, 462).