The Gemara (Sanhedrin 82A), while relating the story of Pinchas killing Zimri, tells us the following:
"And Phineas, the son of Eleazar, the son of Aaron the priest, saw it." (Bamidbar 25:7) Now, what did he see? — Rab said: He saw what was happening and remembered the halachah, and said to him, 'O great-uncle! did you not teach us this on thy descent from Mount Sinai: He who cohabits with a heathen woman is punished by zealots?' He replied. 'He who reads the letter, let him be the agent [to carry out its instructions]'.
According to the Rambam (Hilchot Issurei Biah 12:4), the laws of "He who cohabits with a heathen woman is punished by zealots" is Halacha L'Moshe MiSinai (Sinaitic Law), and support for this can be derived from Pinchas' slaying of Zimri. (I interpret this to mean that we learn the particulars of the Sinaitic Law from the story of Pinchas [e.g. this law only applies if it is committed in public]. I could be wrong.)
In Halacha 5, the Rambam says that "If the zealous person comes to ask permission from the court to slay him, they do not instruct him [to], even if this takes place at the time [of relations]."
The Chidushei HaRim says (English translation here) that the reason for this is a zealot is someone who reacts to a situation instantly and takes immediate action. Pausing to ask Beit Din what to do shows that he is not a true zealot.
So my question is:
Why wasn't Pinchas asking Moshe "'O great-uncle! did you not teach us this on thy descent from Mount Sinai: He who cohabits with a heathen woman is punished by zealots?'" considered asking Beit Din what to do? Doesn't Pinchas stopping to ask Moshe about the law take him out of the catagory of zealot?
Also, if the Beit Din does not tell someone to go and kill the sinner, why does Moshe tell Pinchas "He who reads the letter, let him be the agent [to carry out its instructions]"? Wasn't that Beit Din ruling that Pinchas should kill Zimri?