Shefoch Chamascha is not one of the simanim sections in the beginning of the seder and is not part of the adjacent birkas hamazon or hallel.... Why?
Thank you,
Chaim
"Shefoch Chamascha" is not an official part of the Hagadah. It is a Minhag that came into effect later, after the core text of the Hagadah was canonized. The reason why we say it only after the third Kos is presumably because Nirtzah, the next part of the Hagadah, is all about the Ge'ulah ha'Asidah (the final redemption), which Shefoch Chamascha [most appropriately] precedes.
I ought to add what the Rema writes in Orach Chayim 180: "According to some opinions, one recites Shefoch Chamascha and opens the door in order to remember that it is a 'guarded night.' On the merit of this Emunah, Mashi'ach will come and pour out his wrath on all those who deny Hash-m -- and this is the accepted Minhag."
Wishing you a Chag Kasher v'Same'ach,
Eliezer Chrysler