ROB,
Either a later Bais Din can passul an earlier Bais Din that performed a conversion or it cannot. If, as a rule, a later Bais Din cannot passul the earlier Bais Din, then what Rabbi Goren did was invalid, regardless of his sympathetic motives.
If one agrees that a later Bais Din can passul an earlier Bais that performed a conversion, then whether Rabbi Sherman is right depends on the facts regarding the conduct of the earlier Bais Din, not on a halachic rule.
Reb Moshe, as were many other poskim throughout the ages, was often maikil to be declare that someone was not a mamzer. But being maikel does not mean being “outlandish” or foregoing halacha, chas v’shalom. Being maikel means relying on a shita or a svara, that is valid but that one would not rely on under ordinary circumstances.