SJS,
Great thread! I’ve learned with chasidic litvik charedi rabbis even though I’m MO and it is very valuable. I think our leaders could set the example. Rabbi Matisyahu Solomon has already been to Teaneck, and Rabbi Shlomo Amar visited YU. Can Rabbi Hershel Schachter speak in Lakewood? Can Rabbi Aharon Lichtenstein speak in Bnei Brak?
Rav Soloveitchik z’tz’l had great relationships with Rav Kotler z’tz’l and the Lubavicher Rebbe z’tz’l. That there don’t appear to be such relationships across the divide today may be an example of yeridot hadorot.