Can I extort Launch Party with the creature I'm sacrificing?
No. Basilica Screecher will no longer be on the battlefield when the spell becomes cast, so its ability will not trigger.



Casting a spell:


Placing it on the stack. [CR 601.2a]
Make choices (e.g. modes, targets) that need to be made to cast the spell. [CR 601.2b-d]
Determine the total cost to cast the spell. [CR 601.2e]
Activate mana abilities. [CR 601.2f]
Pay the total cost. [CR 601.2g]


Only once all of the above has happened is the spell cast, so only then would abilities that trigger on casting the spell trigger.


  601.2h Once the steps described in 601.2a–g are completed, the spell becomes cast. Any abilities that trigger when a spell is cast or put onto the stack trigger at this time. If the spell’s controller had priority before casting it, he or she gets priority.


However, you sacrificed Basilica Screecher back in step 5 (601.2g), so it's no longer on the battlefield when you completed the casting of the spell, meaning its ability will not trigger.