Sukkot is the holiday of the 6th to 9th centuries: Hoshanot are from this period, according to Goldschmidt. As is the custom of waving the lulav in 6 directions.
First, Some random 6th -9th century ideas
Guilt and treating the sukkah as exile, not as presense.
Said R’ El’azar bar Maryom: Why do we make a sukkah after Yom Kippur? To teach you that on Rosh Hashanah The Holy One, Blessed Be He, sits in judgment on all mankind, and on Yom Kippur He signs the verdict. Perhaps Israel’s sentence is exile; therefore they make a sukkah and exile themselves from their homes to their sukkah Pesikta of Rav Kahana Parasha 2 addenda, Mandelbaum 457)
Don’t go to Great Adventure or other entertainment for chol hamoed.
The festivals make a difference between the nations and Israel: the nations eat and drink, and go to the circus and the theater, and anger the Lord by their words and deeds; Israel eats and drinks and goes to the houses of prayer to praise His name and to the houses of study to learn His glory. Pesikta 340-1
Vicarious atonement for the nations
Just as this dove atones for sins, so does Israel atone for the nations, for all those seventy bulls which are sacrificed on the festival are on behalf of the seventy nations, so that the world not be bereft of them, as is written (Psalms 109) “They answer my love with accusation but I am all prayer” Midrash Shir Hashirim Rabba 1.
“All seventy bulls that Israel used to sacrifice on the festival were for the seventy nations of the world, so that they not be removed from the world, as it is said: ‘They answer my love with accusation, but I am all prayer’ (Ps. 109:4). That is, now they are protected by prayer instead of sacrifice.” Pesikta de Rav Kahana (par. 30)
And now 1000 years later, three very different fin de siècle 20th century ideas
1] Chief Rabbi Dr Jonathan Sacks writing that the sukkah helps us identify with the poor of “Calcutta and Caracas.” Dignity of Difference 112
2 The sixth Lubavitcher Rebbe, Rabbi Yosef Yitzchak Schneersohn (1880-1950) spoke of seven “chassidic ushpizin” as well: the Baal Shem Tov, the Maggid (Rabbi DovBer of Mezeritch), and the first five rebbes of Chabad: Rabbi Schneur Zalman of Liadi, Rabbi DovBer of Lubavitch, Rabbi Menachem Mendel (the “Tzemach Tzeddek”), Rabbi Shmuel, and Rabbi Sholom DovBer.
Where I was for one or the meals the debate was between the method starting with the Besht or now should they start with the Alter Rebbe and end with the 7th Rebbe. This seems more widespread than I thought. Have the Biblical Ushpizin lost their resonance?
3] Old time R Shlomo Carlebach moving he six directions from cosmology or sefirot to personal experience of religion. link
First, face right. Right in Kabbalah signifies the attribute of hesed, kindness, mercy, overwhelming beneficence. Do you find it too hard to be generous? Or are you suffering from an excess of generosity, of kindness, of love? ”
Then face left. Left in Kabbalah is gevurah – strength, strict judgment, limits. Gevurah is Isaac – bound for sacrifice on Mount Moriah, unflinching, accepting of judgment. Take this opportunity to think of the limits, the judgments in your life. Are your circumstances too confining? Do you need more boundaries, or fewer? Do you need more strength? This is an opportunity to invite God to help you fix the limits in your life.
Next, face straight ahead: tiferet, or beauty. This is the balance, where the beneficence and the boundaries are in their proper proportions. It is Jacob, it is the middle course.
Then, look up. Can you connect with God? What’s the holiness you need in your life? How high can you rise this year?
Then, aim down. This is about groundedness, about your foundations. And it’s about your ability to find the buried treasures, under your feet; the truths buried in the dirt.
Finally, backwards. The essence of repentance is being able to go back and fix your past by your coming to terms with it
I find these three approaches to be quite different: the metonymic ethical, the binding to a saint, and the introspective.