Going to Kevarim on Eruv Rosh HaShanah is not a new minhag. I wish I knew Shulchan Aruch and the Nosei Keilim by heart but I don’t however I have seen it the Minhag written about there see Pri Megadim I believe. Interestingly, the Breslover Chassidim who were in Poland and could not gather in Uman at the time would gather in Chochmei Lublin with Reb Meir Shapiro who was the Baal Tokeah in the Breslov Minyan. He also used to lead them Erev Rosh HaShanah to the grave of the Chozeh because they couldn’t go to Uman.
As far as leaving Eretz Yisrael for kevavrim, the Poskim speak about it:
Birkei Yosef (OC 568:1): If one lives in Eretz Yisrael and desires to prostrate on graves of Tzadikim in Chutz la’Aretz, or he lives in Yerushalayim and desires to go to graves of Tzadikim (elsewhere) in Eretz Yisrael, he may go on condition to return (Pri ha’Aretz 3:6:14, in some editions 3:10:7).
Sedei Chemed (1, Ma’areches Aleph): One may leave Eretz Yisrael to prostrate on the graves of Tzadikim, for it is a great Mitzvah.