The other, heretical, anti-Messianic force was represented by Rav Ovadia Yosef in 5753, whereas the role was played in 5765 by Rav Yosef Shalom Elyashiv. I trust their contributions are well-known.
Again it is true. Anti-Messianic is also Messianic. This is the Sod of Sasson and Simcha, the two heretics. Their heresy is part of the Messianic process, as this process does not happen because of our merit.
Sasson and Simcha are Meshichim. They will bring Moshiach, but it will be in a way they do not expect. About this the GR"A said,
שאילו לא נברא אלא להשגת כוונת חז"ל, בענין ששון ושמחה - דיו
