it seems to me one can bring a smach to the halacha of davka
covering one's head with a talis from the rashi on 12b, d.h. misateif, which clearly says that the
purpose of a talis is akin to that of "blinders", to keep one focused on the
task at hand, i.e. fear of the Almighty, that is, that it must prevent side
glancing, and this is only possible if it covers the head.
Your support for the practice of covering one's head with a Talis while Davening is good. See also Rashi in Kidushin 29b, DH d'Lo Paris, and SHULCHAN ARUCH OC 91:6 (the Shulchan Aruch is just quoting the RAMBAM, Hilchos Tefilah 5:5, and the Kesef Mishnah says that the Rambam's source is the Gemara in Shabbos 10a, regarding being "Mis'atef" while Davening. "Mis'atef" means to cover one's head.).