See the well written article by R Mayer Twerski which basically trashes all your comments.
Which really boils down to point 3 (the reasoning behind the Ramo), which is only about Machashava. The Yodea MaChashavos knows these girls’ Machashavos when putting on Tefillin. You, I, Rabbi Twersky, Dr. Hall and others do not. (As opposed to WoW, where they have stated their own opinion). While I would agree that probably a Bais Yaakov or Charaidi girl who starts may be doing so for other motives, the girls here were tought that this is proper Avodas Hashem by their parents.
(P.S. That is not to say I agree, but to explain why Rabbi Twerski’s points MAY not be valid in this case. Did he speak to the girls in question so that he knows their specific intent? Besides, since Rabbi Twerski is not their Rabbi, the girls (and SAR) have no Halachic imperative to agree with him).