Not that Reb Shlomo needs my limud zchus, but to answer the question of chilul shabbos for kiruv, isn’t it a halacha in shulchan oruch that if non-Jews are trying to be maavir somebody al hadas, you are allowed to be mechalel shabbos, evenn though there is no physical danger, only spiritual danger? Correct me if I’m wrong, as don’t have access now to SH”O.
Secondly, regarding issue of negiah, doesn’t gemara say certain tannaim or amoraim used to dance with the kallah. The students asked aren’t you afraid of the yetzer hara? They answered, domeh alay k’kaki chivri (she is to me like a white dove, i.e., no yetzer hara, only a cheftza shel mitzva). The point is that negiah is only asur bderech chiba, and if they felt there was no chiba, then they were allowed. Perhaps Reb Shlomo felt it was lshem shamayim and not derech chiba, here, as well. Who are we to judge someone who did so much good, and brought so much light into the world?