fabie –
Re: The Vilna Gaon, see Ma’aseh Rav Hashalem, page 276, where the Vilna Gaon is cited as saying reestablishing it would bring the g’ulah closer and that removing the ban was only one of two things he would interrupt his Torah learning and Tefilah, if he would be successful. (The other thing was to reestablish saying Bircas Cohanim every day — which his talmidim in E.Y. were successful in reestablishing.)
As far as Rav Ovadia, I’ve seen him quoted to that effect, but I don’t have a source offhand. You can probably google it.