Who wrote Megilas Esther?

Todays daf (Bava Basra 15) discusses who wrote the various sefarim in Tanach. The Gemara says that the Anshei Knesset Hagedola wrote: Yechezkel, Trei Asar, Daniel, and Esther. Rashi explains that all of these happened in chutz laaretz and לא נתנה נבואה ליכתב בחוץ לארץ. Therefore the אנשי כנסת הגדולה wrote them later in Israel. However, this is contradicted by what is written in Megilas Esther itself where the Megilla writes ויכתוב מרדכי and Rashi comments on that phrase, ויכתוב מרדכי - that Mordechai wrote the Megilla as we have it.

The question is obvious, who wrote Megilas Esther, Mordechai as stated in the Megilla itself or the אנשי כנסת הגדולה as stated by the Gemara?

The Brisker Rav has a brilliant Brisker interpretation which when I first heard it, I thought was fabulous. Now, some years later, this same brilliant explanation seems to be patently ridiculous, and is clearly not what really happened from a historical perspective.

The Brisker Rav explains as follows. The Rambam in Hilchos Megilla leaves out certain dinim (עיבוד לשמה, the way to write the 10 sons of Haman, etc.) that apply to all other sefarim.  On the other hand, the Megilla has other dinim that are the same as a sefer torah. The question is why? The Brisker Rav explains that there are 2 dinim of Megilla.

1. Megilla as a sefer/letter that was written by Mordechai right after Purim. This did not have the status of being part of Tanach. At that time the Chachamim created a chiyuv to read that sefer that Mordechai wrote
2. Megilla as part of Tanach.

Based on this he explains why the Rambam left out certain dinim and included certain dinim in Hilchos Megilla. In Hilchos Megilla the Ramabam is talking about the Megilla as number one above and therefore it doesn't have the regular dinim of a sefer in Tanach, rather it has it's own unique blend because it is a unique entity.

What comes out is that according to the Brisker Rav, Megillas Esther was written twice. The first time, in Shushan by Mordechai, it was not part of Tanach and had no kedusha. However, this is the sefer that we are chayav to read on Purim. Later in Israel the Anshei Knesset Hagedola rewrote the sefer and included it as part of Tanach.

What does it mean that the אנשי כנסת הגדולה wrote the sefer in Israel . The simple understanding of the Gemara in Bava Basra is that they actually rewrote the whole sefer ברוח הקדש as Rashi explicitly writes that they wrote the seforim in Israel and of course it came out word for word the same as what Mordechai wrote.

To summarize, according to the Brisker Rav Megillas Esther was written twice. First it was written right after the events in Shushan by Moredechai. This sefer is what we are commanded to read on Purim. Years later, the אנשי כנסת הגדולה convened and rewrote the sefer ברוח הקדש, and it came out exactly the same to the letter as the original, and made it part of Tanach. So today, we only have 1 Megilas Esther even though it was wriiten independently twice.