The Rebbe was not machmir about waiting until the globe of the moon is fully visible without any clouds at all, but told his followers to recite the berakhah as soon as they could see the moon, even if thin clouds were present.
(Chayei Moharan 483; also see Orach Chaim 426:1)
Reb Noson mentions that singing and dancing at the end of Kiddush Levanah is an expression of simchah, which is the main tikkun for the diminishing of the moon. That is, simchah accomplishes the tikkun ha-malkhus.
(Likkutei Halakhos, Rosh Chodesh 3:4)