Lashon hara is not a problem when it is intended to serve as a benefit to society rather than just as gossip.
As far as the principle of diyun l'chaf zechus (judging favorably), according to the Rambam in his Pirush Mishnayos on the relevant passage in Avos, the obligation of diyun l'chaf zechus applies where an action that was open to interpretation contradicted what was already known of a person's character. You seem to be describing where there is no such ambiguity. Furthermore, even that restriction does not preclude taking necessary precautions where there is a danger to future victims.
In fact, contemporary poskim note that even the more serious prohibition of mesira would not apply in giving over a predator to responsible legal authorities (provided investigations and sentencing are not generally corrupt processes in that society). In fact, remaining silent would be a violation of "lo sa'amod al dam re'echa" ("stand not idly by the blood of thine fellow"), mesaye'a yedei ovrei aveira (aiding and abetting) as well as a chilul hashem (desecrating His name).
Rabbi Yecheil Michel Epstein Aruch Hashulchan Choshen Mishpat 388:7
Note: As is widely known, in times of old in places far away, no person had any assurance in the safety of his life or money because of the pirates and bandits, even if they took upon themselves the form of government. It is known that this is true nowadays in some places in Africa where the government itself is grounded in theft and robbery. One should remind people of the kingdoms in Europe and particularly our ruler the Czar and his predecessors, and the kings of England, who spread their influence over many lands in order that people should have confidence in the security of their body and money. The wealthy do not have to hide themselves so that others will not loot or kill them. On all of this (the presence of looting and killing) hinges the rules of informing (moser) and slandering (malshin) in the talmud and later authorities, as I will explain infra: These rules apply only to one who informs on another to bandits and so endangers that person's money and life, as these bandits chase after the person's body and money, and thus one may use deadly force to save oneself.
Rabbi Waldenberg, Tzitz Eliezer 19:52
Even in the understanding of the secular court system it appears that there is a difference between primitive and enlightened governments as is noted by the Aruch Hashulchan in Choshen Mishpat 388:7 where it states that "every issue related to informing found in the Talmud and poskim deals with those far away places where no one was secure in his money or body because of bandits and pirates, even those who had authority, as we know nowadays in places like Africa" such is not the case in Europe, as the Aruch Hashulchan notes...I write this as a notation of general importance in the matter of the laws of informing.
See, however, Iggrot Moshe Orach Chaim 5:9(11) who [according to the aforementioned site] writes:
It is prohibited for us to inform on a person for a matter where the
punishment is unfounded in Jewish law. In Jewish law, theft is
resolved through restitution as measured by an expert, and secular law
punishes through imprisonment, unfounded in Jewish law.