The work of Rohault de Fleury, "Mémoire sur les instruments de la Passion" (Paris, 1870), deserves more prolonged attention; its author has sought out with great care and learning all the relics of the True Cross, drawn up a catalogue of them, and, thanks to this labour, he has succeeded in showing that, in spite of what various Protestant or Rationalistic authors have pretended, the fragments of the Cross brought together again would not only not "be comparable in bulk to a battleship", but would not reach one-third that of a cross ...
The Orthodox tradition regarding the True Cross gives a clear account that the Cross was deliberately cut up into pieces and distributed throughout the Empire after its capture by the Persians and subsequent recovery. The Church did want a relic of such great importance ever to fall completely into the hands of non-Christians again.
One thing I noticed in the New Advent article you linked to was that the Cross was speculated to be made of pine. An interesting Orthodox Tradition is that it was made up of three different kinds of wood: pine, cedar, and cypress. It alludes to Isaiah 60:13 in the LXX as a prophecy of this.
I had not heard of the work of de Fleury -- I never doubted that the rationastic stories about the relics of the True Cross were gross exaggerations with a definite agenda, but I hadn't learned that anyone had done the work to disprove such tales.