Non-egalitarian approach to female scribes
Megillot and sifrei neviim
Since megillot and other scrolls for ritual use are not explicitly described as being invalidated when written by women (or minors, etc), it is perfectly reasonable to say that therefore the rule does not apply. By analogy with tzitzit, any Jew could write a megillah. (By analogy with succah, a non-Jew could also write a megillah; further study would be required.) On the other hand, since other scrolls are generally held to work pretty much like sifrei Torah (in almost all aspects of manufacture, for instance), it is also perfectly reasonable to say that the rule does apply, and hence that women may not write such scrolls. Valid arguments have been, and may be, made in either direction, and the decision is one to be made by individual communities.
Rabbi Ross Singer published an article to this effect in the Edah journal, concluding that "the majority of authorities and the weight of halakhic reasoning point towards considering women eligible to write Megillot Esther." I have reproduced the article on this site in HTML format.
Enabling women to write sifrei Torah, tefillin and mezuzot
When faced with any intractable halakhic ruling, there are two options. One can accept the ruling as is, or one can seek a way to absorb the ruling into one's halakhic system but limit or expand its scope in some way, in order to render it more palatable.
Accepting, in this case, involves agreeing that women are invalid to write sifrei Torah, tefillin and mezuzot, and refraining from becoming involved with such items which were written by women.
Absorbing entails expanding or limiting ("redefining") the scope of a concept.
The mechanism of Jewish law works a bit like higher mathematics. You have known, accepted data that you cannot change, whether it is previously-proved theorems or Talmudic texts. You have a question. You know jolly well what you want the answer to be, and you put your data together in creative ways until you find a way of demonstrating your answer. Sometimes it is impossible, but often enough it is possible (the saga of Fermat's Last Theorem provides a fine analogy, but we won't get into that here) provided you apply your data in sufficiently creative ways. The halakhic literature, from the Talmud onwards, is crammed full of examples of halakhic process working in just this way.
This philosophy of halakha makes halakhic idealists very angry. Halakhic idealists want halakha to work like a calculator - you put in your data, ask your question, and out pops the answer, the same every time. This is like the person who responds "STUPID" to the old joke "There are only 10 sorts of people in the world: those who understand binary and those who don't." If you are an halakhic idealist, you will hate the rest of this page. That's fine, you're allowed to hate it. Just please don't send me angry emails, okay? They get boring.
Application to sifrei kodesh
Here are some ways of applying the existing data to sifrei kodesh.
1. Some halakhists have redefined sefer Torah, in the following manner: "In the old days, they knew exactly how the Torah went, every single letter. That was the only authentic Torah – one written with the authentic spellings, written on authentically processed parchment, and so on. Nowadays, we don't have an authentic Torah – we've lost the traditions regarding spelling (this is true), parchment processing (this is also true), and so on, so what we have is at best a "sefer Torah" - an imitation, a best guess. We keep going, because otherwise we'd lose the Torah entirely, but we don't have the original. The statements in the Talmud are talking about the original sefer Torah; since we only have a "sefer Torah" we need not be so stringent in applying the Talmudic rules."
The Shaagat Aryeh, the Kol Bo and the Abudraham are notable propagators of this approach (not all in the context of women). Its potential problems are very many, but not necessarily insurmountable – simply that any justification based on this approach must take care to seek out the potential problems and meet them satisfactorily. Further, this argument is only made of sifrei Torah – not of tefillin or mezuzot – so this approach can enable women to write sifrei Torah only, not tefillin or mezuzot.
2. Other halakhists have redefined obligation. The prevailing position is to regard obligations accepted voluntarily as having a far lesser import than obligations acquired by birth, therefore meaning that someone with a voluntary obligation cannot serve as a proxy for someone born with that obligation. Redefining obligation entails proving that if someone accepts an obligation upon themselves, they are to be considered just as obliged to carry it out as is someone born with that obligation – somewhat as one who becomes a citizen of a particular country is to be considered just as much a citizen as one who was born there – and therefore eligible to serve as proxy.
Taking this interpretation, any woman who accepts upon herself as binding the obligation to lay tefillin (and it should be noted that this does not mean that she does it now and again, it means she commits to doing it on every single relevant day for the rest of her life, and if she fails to do so, considers herself as having committed a grave transgression) can be considered just as obligated as a regular Jewish adult male. This, as we have seen, renders her eligible to write tefillin, mezuzot and sifrei Torah.
This position is supported by certain references in, for example, the Yad Ephraim, talking about the potential validity of voluntary obligation.
See the page May a Woman Write a Mezuzah? for an application of this princicple.
3. Another group of halakhists has redefined woman, suggesting that "woman" in the Gemara refers to someone with the set of "women's obligations" conceived of by the halakhic system – thus setting women who accept extra obligations into a different category. Alternatively, it is suggested that "today's woman" is a different creature entirely from the "woman" conceived of by the early rabbis. This is a brave attempt, if not altogether compelling.
People's attitudes are a very strong factor in halakhic decision-making. Regarding public Torah reading, authoritative sources say (essentially) "Women can read the Torah in public, it's just not nice." It took Mendel Shapiro fifty-some pages to argue that "it's not nice" is a subjective statement, and women read Torah in only a tiny handful of non-egalitarian communities, because generally the feeling is that women shouldn't read Torah. The feeling is the same regarding female scribes, and the authoritative sources are not nearly as easy to argue with.
Accordingly, any non-egalitarian woman who wants to write Torah is going to need a lot more than fifty pages to justify her rationale, and she's going to have her work cut out changing public opinion. The page count available online basically starts in 2004 with R' Ross Singer's aforementioned EDAH ">article on women writing Megillah and continues in 2006 with his JOFA article (scroll to page 4) on women and safrut generally. R' Dov Linzer and I add to it in Meorot in 2007, me arguing (surprise) for women writing Torahs, and R' Linzer efficiently defending the status quo. I'm personally no longer interested in habituating non-egalitarian frameworks, so I'm not adding to that conversation any more, but someone else will, eventually, I expect. Give it a few generations.