Bar krisus for Kesivas HaGet - 2

We posted here regarding the issue of whether one needs to be a bar krisus to write a get or not. In that post we pointed out that Rashi seems to imply that one needs to be a bar krisus. What is strange about Rashi, however, is that he quotes a drasha that doesn't seem to be found anywhere. Rashi says that since the pasuk says V'kasav v'nasan, so we learn from there that one needs to be a "bar nesinah" of a get in order to be a "bar kesiva". There is another gemara in Gittin that discusses another very similar drasha of "ukshartem uchsavtem" that to write tefillin (and by extension sefer torah and mezuzah) one needs to be a "bar keshira" or one who in general would wear tefillin. The rishonim argue as to how far we expand this drasha. I once thought to suggest that Rashi holds like those rishonim who take a very expanded view of this drasha and applies the same exact drasha to v'kasav v'nasan. In other words, the source of Rashi's drasha on 9b in Gittin of V'kasav V'nasan is actually the later gemara in gittin regarding the writing of ST"aM. If this is the case then we will have to deal with why tosafos never brings the case of ST"aM as a proof that one does need to be a bar krisus to write a get, and instead brings the case of bris milah to prove that just like one need not be a bar bris milah to perform a milah, so too he need not be a bar krisus to write a get. Even further, milah seems to be totally different because there it's the actual maaseh milah that is being done. Here by the writing of the get, that is only a "hechsher" for the maaseh gerushin. Wouldn't it be much better to bring a proof from the writing of STa"M which is also a "hechsher" towards the actual mitzvah? It occured to me to answer this question by pointing out that R' Soloveitchick held within some rishonim that the writing of a get is actually the "haschalas gerushin" at some level. It is not a mere hechsher (as would be the pashtus), but, rather, a beginning of the kinyan. If tosafos held like this the comparison from milah makes perfect sense. Both are part of the actual maaseh, and not mere hechsherim. In future installments we will iy"h expand upon these ideas.