1. Actually Rambam (Hilchot Gerushin 2:20) says that beating him gets rid of his yetzer hara. However, Rambam lived in a time when the Jewish communities had internal autonomy and the bet din was the officially recognized. Outside of Israel, where the Chief Rabbinate courts handle marriage and divorce for Jews(and have various means of persuasion at their disposal, including imprisonment, but not corporal punishment), there is no longer an official bet din (bet din kavua). Certainly, three rabbis who hang out a shingle, do not constitute a bet din kavua.
2. In the US no one has a halachic obligation to recognize this or that bet din. In fact, I heard that there are several people in Monsey who were put in cherem by one community but receive all honors in their own shuls.
3. There is no mitzva to have a person beaten in order to extract a get from him. It is an option that a bet din kavua has. Thus doing it is a chillul Hashem. This is similar to returning a lost object to a gentile where it is expected that people will return lost objects.
4. Applying social pressure probably does not constitute force as he can choose to ignore it. The same goes for informing his employer. However, the bet din or other organization should be careful to run afoul of the libel and slander laws.
5. Once someone in Posen became a Reformer so Rabbi Akiva Eiger, upon the wife’s request, ordered him to give a get. He refused so RAE read him the first mishna in Kiddushin regarding how a married woman becomes single. The guy laughed, walked out of the office and fell down the stairs.