Parent bullets to game area?

I’m currently working on a 2D scrolling shooter, but I want it to be a bit more visually impressive. So I’ve put my player object inside another object that I call Gameplay Area. I’ve managed to make the GA object move along an iTween path, and I’ve managed to make the player object fire projectiles.
However, the player object fires the projectiles in worldspace, but I want to make him fire them in GameplayArea-space.

The result is what you can see in the image above.
Yes, that’s right, the white dots are trails left by the the projectiles, to visualise the problem. Fine in a fully fledged 3D flight sim, AWFUL for a “2D” shooter
And of course, I do realise that the problem will carry across to enemy aircraft.

I started coding in Unity literally yesterday, so I feel proud of the results I have so far. I do realise that I somehow have to parent the projectiles to the gameplay area object, but I just don’t have a clue on how to do so.

Gameobject go = Instantiate(obj,pos,rot);
go.transform.parent = GA;

Something like that?

I’m writing in C#, and if I’m not mistaken, that’s Javascript?
Currently, the script on the bullet is as follows:
using UnityEngine;
using System.Collections;

public class Projectile : MonoBehaviour {
	public float ProjectileSpeed;

	// Use this for initialization
	void Start () {
		transform.parent = "GameplayArea";
	}
	
	// Update is called once per frame
	void Update () {
		float amtToMove = ProjectileSpeed * Time.deltaTime;
		transform.Translate (Vector3.back * amtToMove);
	}
}