Is Mama Ruchel Really Buried In Kever Rachel and When Is her real Yurzeit?

According to the פסיקתא רבתי Rochel Imeinu died between Pesach and Shavuois when the ground was dry (see Rashi Bereishis 48:7 who seems to agree)

The ילקוט שמעוני writes that she died on the 11th of Cheshvan.

In one of the "Dead Sea Scrolls," it is written that she died on the 10th of Teves.

So where is she really buried??

We all know that Kever Rochel is in Bais Lechem, 10 kilometers south of Yerushalyim.

According to some Rishonim 
רלב''ג, חזקוני, רמבן פרשת ויחי 
Kever Rochel is not in the Bais Lechem we know, but in רמה north of Yerushalyim!

(1) In Shmuel Alef י'  ב' it is written that 
קברת רחל בגבול בנימין  
Bais Lechem is in Yehuda .... not Binyamin.

(2) Rashi in פרשת ויחי quotes the פסיקתא רבתי  
"Yaakov told Yosef that he buried Rochel on the road ע''פ הדיבור" so that in the future she would daven for her children when Nevuzraden would forcibly take them from Bavel.
And as they pass her Kever .... Rochel will come out and cry 
רחל מבכה על בניה 

If Kever Rochel is in the Bais Lechem we know, why would they be passing her Kever on the way to Bavel which is north of Yerushalyim?

(3) See the ספרי  פרשת וזאת הברכה, פסקא שנ''ב  
where it is written 
ר' מאיר אומר בחלקו של בנה מתה 
Rochel died in her son's chelik ...which is in the chelik of Binyamin and not in the chelik of Yehuda where our Bais Lechem is situated.

The חזקוני explains that it was an honor for Rochel to be buried in
her children's chelik .

Hat Tip: MF