HaGaon HaRav Elimelech Bluth shlita, a talmid muvik of Rav Moshe, says in the name of Rav Moshe that before the war engaged couples did *not meet at all*, and that the current minhag of them only not meeting during the last week of the engagement is a new kula that developed due to yeridos hadoros.
Nisuin Kehilchaso mentions the minhag of a Choson and Kallah not seeing each other from the conclusion of the shidduch until the Chupa. His sources include Shu”t Maharshdam, Pele Yoetz and Elah Hamitzvos. The minhag of not seeing each other after the engagement is recorded to have existed in many communities at least dating as far back as 1228 and in Yerushalayim in 1730.
Rav Shach and Rav Shternbuch have said that engaged couples today should not meet more than once every three or four weeks. Rav Elyashiv ruled that during the seven days before the wedding the Choson and Kallah should neither see each other nor speak on the telephone.
The three children of Rav Yaakov Kamenetsky did not see their future spouses the week before the wedding. And a fourth, Rav Avraham Kamenetsky, reported that when he asked his father about speaking to his kallah on the phone during the week before his wedding, he was advised against it.