In my earlier post I wrote that the Ashkenazi Sofrim stretched the lines possibly because of Zeh Keili VeanVeihu, that is, because it looks nicer. I did some further research into this and in turns out that this is already suggested by the Ran (Rabbeinu Nissim, 990–1062), who seem to say that the two columns of Haazinu and also Bnei Haman in Megilat Esther should be perfectly symmetrical (click here for full commentary):
פירוש כשהחומה שוה בשני ראשיה ואין בה בליטות אין להוסיף עליה כמו אם היו שם בליטות ושיני החומה שאז יוכלו להוסיף על הבנין
ודאי שהיה בזה קפידא ומהראוי לתקן ולמשוך השורות
ועלה בדעתי להעמיד מלת הצור שבשיטה שאחריו למעלה להשוות השיטות
The Maharam DiLuzanu however disagrees and claims that the Ran was not implying that all sides should be symmetrical - the Ran was solely referring to the column of Bnei Haman to the left, which is always perfectly symmetrical:
The Minchat Yitzhak [1902-1989] has a responsa about this and brings more sources, finally concluding that for Hiddur Mitzva, the columns in both Haazinu and Bnei Haman should be symmetrical, but he strongly disagrees with other commentators who raised the possibility of this being Leicuva, mandatory. It's a pity I only came across this now, as I already wrote my Megillat Esther not symmetrically(see here)..
But this conclusion is only valid for Ashkenazi Jews, as the Ran wasn't categorical about this and both the Noda BiYuda and Minchat Yitzhak are Ashkenazi. The Yemenite Jews evidently disagree with this idea, as their Torah have completely asymmetric Hazinu columns. And as noted in my other post, they are supported by the Aleppo Codex, which means that their version is most certainly the correct one. So my Megillat Esther could have been written symmetrically, but perhaps through my mistake, I actually wrote the very best pattern after all?