[Avodah] Old style Hallel

[Gilad Field]

I was learning Rambam hilchos chanukkah with one of my kids last night and
the following halacha caught my eye. The Rambam discusses the way hallel
used to be said in the olden times (before the time of the Rambam). and he
describes how the chazan would recite the words and everone would respond
"halleluka". At the end the Rambam gives a mnemonic device to remember
how many times the people would respond "halleluka" - 123 times based
on the years of Aharon HaKohen.

I was puzzled by this comment. First of all it is rare that the Rambam
would use a siman in this way (i.e. as a mnemonic device), I did a quick
search in the Bar Ilan and Rambam only uses a siman as a memory tool 7
times (and 4 of them are in hilchos kidduah haChodesh). I am not sure if
that is significant at all - but since the Yad is a halacha sefer I wonder
why he chose to include it if it does not serve any halachik purpose.

In addition if you look up the source of the Ramabam , which according to
the Magid Mishnah is Midrash Tehillim, there Rebbi Yehoshua ben Levi is
basically saying he never looks in Aggadic sources, but he did this one
time -- and he regrets it! (the Or Samayach points out that the Yershalmi
in the beginning of the 16th perek in shabbos, and others point out the
16th perek of maseches sofrim) which stregthens the question as to why
Rambam included this mnemonic.

Has anybody come across any interesting explanations of this Rambam? I
know there is a chasam sofer (Sukkah, 38a) that does try to explain -
but I really don't understand what he is saying:

עונה אחריו הללוי'. כ' רמב"ם פ"ג מהל' חנוכה קכ"ג פעמים הללויה עוני' בהלל
סי' לדבר שנותיו של אהרן הכהן ע"ש ממס' סופרים דע הלל גמטרי' אדני הללוי'
גמטרי' אלקי' אדני אלהים היינו ב' היהי"ן דהוי"ה ית"ש שנקראו בסוד לאה רחל
גמטרי' ער"ד בקדושה וכשתוסף על מספר הלל הללויה הנ"ל מספר קכ"ג עולה ער"ד
ע"כ במיתת אהרן וישמע הכנעני מלך ער"ד בטומאה וא"א לפרש יותר:

Gilad