I don't understand in your eein part , the mysah rav with the elders of Sidon if there were 2 elders each one performing something different how would it be a ryah to the rambam ? And also in the beis halevi regarding spending more then one third , the reason given doesn't explain why so much MORE then one third Was RECOMENDED by chazal? (Could be u guys did and I'm just not understanding properly )
Yosef, Isreal
1) The Gra holds that the the two Amora'im from Eretz Yisrael have a fundamental Machlokes about how to perform Mehadrin Min ha'Mehadrin. According to the opinion of k'Neged Yamim ha'Nichnasin, the goal every night is to demonstrate the number of days of the Nes that have occurred.
The correct way to perform Mehadrin Min ha'Mehadrin according to this Shitah is by having no more than one Hadlakah per house. Tosfos holds like the first opinion. Only one person lights one "Chanukiyah" per house, leaving no room for confusion about what night of Chanukah it is.
The Amora who says Ma'alin b'Kodesh holds that we are to be Mefarsem only that the Nes increased every day and we do not have to light in a way that demonstrates the day of the Nes. A family of five lights five Neros on the first day, ten candles on the second day, and so on.
The Gra infers from the Rif's citing of the "Ma'aseh Rav" of the two Zekenim in Tzidon, who held like the second Amora, that the Rif rules like the second Amora. The Rambam holds like the Rif.
2) I understand the Beis ha'Levi as saying that without the Nes the Neros would have been smaller, yet sufficient to be Mekayem the Mitzvah of Hadlakas ha'Menorah. The Nes was exclusively one of Hidur since they had enough oil to perform the basic Mitzvah with smaller wicks.
We highlight the fact that the Nes was an "upgrade" in the Hidur of the Ner rather than one that enabled them to perform the basic Mitzvah by lighting Mehadrin and Mehadrin Min ha'Mehadrin, a manner of Hidur not found in other Mitzvos.
I hope this is helpful.
Avraham Phillips