I am having difficulties with the Gemara on Lulav on Shabbos and would like some help

Short synopsis of the Gemara

Mishnah: Sukah 42b

If the first of Sukos is on Shabbos we use the Lulav but not if Shabbos is during Chol ha'Mo'ed If Hoshana Raba is one Shabbos we use the Aravah but not if Shabbos is another day of Sukos

Gemara: Why not use the Lulav on Shabbos - because of the Gezeirah of Rabah that perhaps some will carry the Lulav on Shabbos and carry 4 Amos in Reshus ha'Rabim If so why not prohibit it on the first day if it is Shabbos? Since the first day is from the Torah even outside the Beis Hamikdash they didn't prohibit it If so why is it prohibited outside of Israel? Because we don't know the exact date (obviously before the fixed calendar} but in Eretz Yisrael where they know the true date of Sukos they use the Lulav Conclusion (temporary) in Eretz Yisrael the Lulav is carried the first day even on Shabbos (43a)

The Gemara brings a proof from 2 Beraisos one that says they brought the Lulavim to the Beis Hamikdash and one says to the Beis ha'Keneses. So we see that even later they used the Lulav on Shabbos

On 43b the Gemara discusses Aravah with a similar discussion. There Bar Hedya who came from Eretz Yisrael answered that Hoshana Rabah never comes out on Shabbos. When Ravin came from Eretz Yisrael he said that Hoshana Rabah does come out on Shabbos

On the top pf 44a the Gemara (because of some questions) reverses itself and says that since outside of Eretz Yisrael the don't use the Lulav on Shabbos so also inside Eretz Yisrael. The Gemara now answers the contradiction of the Beraisos that the one talking about Beis ha'Keneses is while the Temple stood but outside of Jerusalem/Beis Hamikdash

Questions:

1. How can there be a Machlokes between Bar Hedya and Ravin whether Hoshana Rabah actually falls on Shabbos - its a factual question. Furthermore why rely on these people coming from Eretz Yisrael. Even the Babylonians eventually found out when RH was and hence Hoshana Rabah (and in fact Hoshana Rabah on the 21st most communities knew in time). Of course we know that with the fixed calendar Hoshana Rabah cannot fall on Shabbos like Bar Hedya.

2. Technical problem that "Lo Sisgodedu" doesn't apply to two countries. see http://www.dafyomi.co.il/sukah/insites/su-dt-044.htm for some answers

3. Eretz Yisrael keeps one day Yom Tov while Bavel keeps 2 days from the above Daf in the name of the Lechem Mishneh "The Rabanan do not institute an active practice, a "Kum v'Aseh," such as the requirement for the Jews in Eretz Yisrael to observe a second day of Yom Tov" However, this is exactly the later Takanah when there was no longer a Safek that Jews outside Eretz Yisrael do keep 2 days. So they did institute a "Kum Aseh" when they wanted to.

Rabbi Kornfeld answers that for Lulav there is both Lo Sisgodedu and the Gezeirah of Rabah while for 2nd day Yom Tov there is only lo Sisgodedu. Rabbi Kornfeld assumes that there Gezeirah was right after the Churban which is hard to accept and again the Yerushalmi knows nothing of the Gezeirah of Rabah and we are talking about the practice in Eretz Yisrael

4. How does the Gemara change its mind a full Blatt later? Again whether Eretz Yisrael used the Lulav on the first day that was a Shabbos is a factual question. The Yerushalmi doesn't seem to mention any such Gezeirah.

When did this Gezeirah occur? Mefarshim seem to assume at the time of the destruction of the Temple. To me it is inconceivable that the Tana'im who were overwhelming from Eretz Yisrael with very few exceptions would have prohibited Lulav in Eretz Yisrael because of problems that the Babylonians had because of Safek. As mentioned there is no hint of this in either Tanaitic literature or the Yerushalmi. We know the fight the sages of Eretz Yisrael gave when Chananyah wanted to perform Kiddush ha'Chodesh in Bavel and they insisted on the priority of Eretz Yisrael. The center of rabbinic Jewry was in Bavel only in Amora'ic times. Even early Amora'im like R. Yochanan stressed the superiority of Eretz Yisrael and it is unlikely they would change the custom in Eretz Yisrael for the Babylonians.

For those that use the logic of a "Stam" Gemara, there is no names mentioned in this Sugya hinting that in fact it may be a very late Gemara perhaps after a fixed calendar was introduced As an aside the Gemara answered that one Beraisa was talking about a Beis ha'Keneses outside of the Temple. Some historians deny that Batei ha'Keneses existed outside of Jerusalem until after the Churban.

In fact some groups are trying to reinstitute Lulav in Eretz Yisrael this year when the first day falls on Shabbos.

However, my question is Pshat in the Gemara and not Halachah l'Ma'aseh.

Chag Same'ach