It seems the Talmidim of the GR"A have been counting seven Pekidot and started with 5500. I doubt this comes from the GR"A. Perhaps he was misunderstood. For one, the GR"A knew very well that one year must be added.
When we count properly, the penultimate Pekidah was in 5753, the year that brought the Oslo accords.
The reason for the 36 years is clear now, 288 = 36*8. The Gaon spoke the truth.
עת הזמיר הגיע, עת הזמיר באה בשבע הפקידות דאתחלתא
Kol HaTor 5, 1, 10
הכרח שנשמתו של משיח תרד לעולם בעקיפין
HaTekufa HaGedola, p. 534 (Yerushalayim, 5761)