Megillah as kitvei kodesh (II) - can a woman write a megillah?

With respect to writing Sifrei Torah, tefillin, and mezuzos (STA"M) the gemara derives from the juxtoposition of the mitzva of kesiva to the mitzva of tefillin that whomever is not obligated in "u'kshartam", tying tefillin, is not obligated in "u'ksavtam", in writing. Therefore, women, who are not obligated in tefillin are psulos to write STA"M. The achronim debate whether this same psul applies to writing the megillah. R' Akiva Eiger (siman 691) lumps everything together, while the Birkei Yosef distinguishes - since women are indeed obliagted in reading the megillah, they are ksheiros to write it as well.
Perhaps this issue depends on the 2 dinim developed by the Brisker Rav (see previous post). If the psul of an isha is a disqualification of her writing per se as kesiva, then even for kesivas megillah her writing is not considered writing. But if the disqualification is based on her writing being disqualified from having kedushas STA"M, then megillah may be different because the dinim of kedushas kitvei kodesh are not derived from STA"M to megillah.