Local translation error

Hi. As a quick project I've decided to try to make something akin to Wing War, a basic multiplayer flight game.

To achieve this, I've created a "play field" object, where all of the planes are local objects. I move them around the play area using transform.translate. The play field moves through the game world and rotates.

Now, even though the planes are set to translate in the local X and Y axis, they end up moving in the Z-plane.

 using System;
 using System.Collections;
 using System.Collections.Generic;
 using UnityEngine;
 
 public class DuelManager : MonoBehaviour
 {
     public GameObject Camera;
     public float CameraSpeed;
     public Transform LookAtPosition;
     public float ForwardSpeed;
     public float XSpeed;
     public float YSpeed;
 
     public AnimationCurve CenterCurve;
 
     public float XBounds;
     public float YBounds;
 
     public float Timer;
     public float TurnDuration;
     public float AverageX;
     public float AverageY;
     public int CurrentAttacker;
     [Serializable]
     public struct Players
     {
         public string PlayerName;
         public Color PlayerColor;
         public GameObject Plane;
         public Input Horizontal;
         public Input Vertical;
         public Input Trigger;
         public float XCoordinate;
         public float YCoordinate;
     }
     [SerializeField]
     public Players[] players;
 
 
     // Start is called before the first frame update
     void Start()
     {
         
     }
 
     // Update is called once per frame
     void FixedUpdate()
     {
         AverageX = 0;
         AverageY = 0;
         transform.Translate(transform.forward * Time.deltaTime* ForwardSpeed,Space.World);
 
         
         Camera.transform.localPosition = Vector3.Lerp(Camera.transform.localPosition, new Vector3(players[CurrentAttacker].Plane.transform.localPosition.x, players[CurrentAttacker].Plane.transform.localPosition.y+10, -10), Time.time*CameraSpeed);
 
         
 
         if (players[1].Plane.transform.localPosition.x >= 0)
         {
             players[1].Plane.transform.Translate(transform.right * Time.deltaTime* -CenterCurve.Evaluate(players[1].Plane.transform.localPosition.x), Space.Self);
         }
         else
         {
             players[1].Plane.transform.Translate(transform.right * Time.deltaTime * CenterCurve.Evaluate(-players[1].Plane.transform.localPosition.x), Space.Self);
         }
 
         players[1].Plane.transform.Translate(transform.right * Time.deltaTime * Input.GetAxis("Horizontal") * XSpeed, Space.Self);
         players[1].Plane.transform.Translate(transform.up * Time.deltaTime * -Input.GetAxis("Vertical") * YSpeed, Space.Self);
 
         players[1].Plane.transform.localPosition = new Vector3(players[1].Plane.transform.localPosition.x, players[1].Plane.transform.localPosition.y, 50);
 
         for (int i = 0; i < players.Length; i++)
         {
             if (i == CurrentAttacker)
             {
 
             }
             else
             {
                 AverageX += players[i].Plane.transform.localPosition.x;
                 AverageY += players[i].Plane.transform.localPosition.y;
             }
         }
 
     
 
 
         AverageX = AverageX / players.Length-1;
         AverageY = AverageY / players.Length-1;
         LookAtPosition.localPosition = new Vector3(AverageX, AverageY, 50);
 
    
             Camera.transform.LookAt(LookAtPosition.position);
 
 
         transform.Rotate(0, AverageX*0.01f, 0, Space.World);
 
 
     }
 }
 

In the above code, I force the plane to its correct Z-position on every frame, which initially seems to fix the problem. However, once the play field approaches a rotation of 90 degrees, movement becomes sluggish and the aircraft centering feature goes berserk. I can't figure out why this is as the plane continues to have a rotation of 0,0,0.

For reference, here's a video of what happens:: Video

Any ideas?