Regarding the count instituted by the GR"A, 5500 + a*n, where a=250/7, approximately 36 years, this is the final piece of the count m(n) = 4000+a*n, counting the years of Moshiach according to Chazal, according to Torat HaNigleh. The year 5750 was the year m(49) according to this, and we live now deep into the final period, which ends with 5786 = m(50). The count 5500 + a*n is the final stretch, m(42) + a*n. The parallel with the Omer count is obvious.
There is a deep reason why the GR"A instituted in fact the count m(n) = 5501 + a*n, where a is exactly 36 years. Now, m(7) is 5753, and m(8) is 5789. The deep reason is related to the secret of 288, which the GR"A at some level must have known. From his Talmidim, we learn the first version. The wise will understand.
