Why is the hard limit for the size of a beis din 71 members?

Question

When a beis din is undecided (e.g. when adjudicating monetary cases or Dinei Nefashos), judges can be added until the beis din reaches a maximum size of 71.

Why is a beis din's maximum size 71? Why what does the number 71 symbolize?

Source for the halacha (link):

רמב"ם הלכות סנהדרין פרק ח

אחד אומר זכאי ואחד אומר חייב ואחד אומר איני יודע... היו מחצה למחצה ואחד אומר איני יודע הרי אלו מוסיפין שנים אחרים, וכן אם נסתפק הדבר מוסיפין והולכין עד שבעים ואחד, הגיעו לשבעים ואחד ואמרו שלשים וחמשה חייב ושלשים וחמשה זכאי ואחד אומר איני יודע נושאים ונותנים עמו עד שיחזור לדברי הצד האחד.

Halacha 2

The following laws apply when there is a difference of opinion within a court of three judges with regard to a monetary issue… If one says that his claim should be vindicated and one says he is liable… and the third judge says: "I do not know," we add another two judges. Thus five judges debate the matter…
If, in this situation as well, the opinions are evenly balanced and one says: "I don't know," or in any situation that there is a doubt, we continue to add two more judges until we reach 71 judges. If, after reaching 71, the issue is still unresolved, i.e., 35 hold him liable, and 35 wish to vindicate his claim and one says: "I don't know," they debate the matter until the judge who has not made up his mind sides with one of the opinions…

Answer 1

The RaMBa"M is likely quoting this directly from the Gemara in Sanhedrin 2A (Hebrew, English):

סנהדרין גדולה היתה של שבעים ואחד וקטנה של עשרים ושלשה מנין לגדולה שהיא של שבעים ואחד שנאמר אספה לי שבעים איש מזקני ישראל ומשה על גביהן ר' יהודה אומר שבעים

The Great Sanhedrin consisted of seventy-one members; the small sanhedrin of twenty-three. Whence do we deduce that the Great Sanhedrin is of seventy-one? — it is said, gather unto Me seventy men (Bamidbar 11:16); with Moshe at their head we have seventy-one. R. Judah said it consisted only of seventy.

As to the significance of the number seventy in the pasuq (Bamidbar 11:16), I found the following three explanations via Chabad.org (link) and Yalqut Shim'oni directly:

Midrash Rabbah, Beha'alotekha 15:19 (Hebrew link)

Moses thought: What shall I do? If I bring five from each tribe, the total will not amount to seventy and there will only be sixty. If I bring six from each tribe, there will be two more than seventy. If I bring six from one tribe and five from another, I will introduce jealousy between one tribe and another.

What did he do? He took seventy-two ballots and wrote on seventy of them "elder" and two ballots he left blank. Then he mixed them up in an urn and proclaimed: "Come and draw your ballots." A man who drew out a ballot inscribed with the word "elder" knew that he had been appointed an elder. And one who drew out a blank knew that he had not been appointed, and the superintendent would say to him: "There is still a ballot in the urn inscribed with the word 'elder'; had you been worthy of being appointed you would have drawn it."

Yalqut Shim'oni, Beha'alotekha (Hebrew link)

כנגד שבעים ימים טובים שנתן להם הקב״ה. ואלו הן שבעה [ימי פסח ושמונה] ימי החג וראש השנה ויום הכפורים ועצרת ונ״ב שבתות הרי שבעים

The seventy elders correspond to the seventy Yamim Tovim HQB"H gave them: seven [days of Pesahh], eight [days of Sukkot], Rosh Hashanah, Yom Kippur and Shavu'ot, along with 52 Shabbatatot, which is 70.

דבר אחר כנגד ע׳ נפש שירדו למצרים

Another interpretation is [that the seventy elders] correspond to the seventy who descended to Egypt.