Apparently the manual list of connected players wasn't updating, so I've switched to just use the NetworkManager's list instead.

Assets/Scripts/Game/InGame/InGameRunner.cs

         private Queue<Vector2> m_pendingSymbolPositions = new Queue<Vector2>();
         private float m_symbolSpawnTimer = 0.5f; // Initial time buffer to ensure connectivity before loading objects.
 
-        [SerializeField] private NetworkObject m_playerCursorPrefab;
-        [SerializeField] private NetworkObject m_symbolContainerPrefab;
+        [SerializeField] private NetworkObject m_playerCursorPrefab = default;
+        [SerializeField] private NetworkObject m_symbolContainerPrefab = default;
-        [SerializeField] private NetworkObject m_symbolObjectPrefab;
-        [SerializeField] private SequenceSelector m_sequenceSelector;
+        [SerializeField] private NetworkObject m_symbolObjectPrefab = default;
+        [SerializeField] private SequenceSelector m_sequenceSelector = default;
-        private NetworkList<ulong> m_connectedPlayerIds;
         private ulong m_localId; // This is not necessarily the same as the OwnerClientId, since all clients will see all spawned objects regardless of ownership.
 
         public void Initialize(Action onConnectionVerified, int expectedPlayerCount)
 
         private void FinishInitialize()
         {
-            if (m_connectedPlayerIds != null)
-                m_connectedPlayerIds.Clear();
-            else
-                m_connectedPlayerIds = new NetworkList<ulong>();
             m_symbolContainerInstance = NetworkObject.Instantiate(m_symbolContainerPrefab).transform;
             ResetPendingSymbolPositions();
         }
             playerCursor.SpawnWithOwnership(clientId);
             playerCursor.name += clientId;
 
-            if (!m_connectedPlayerIds.Contains(clientId))
-                m_connectedPlayerIds.Add(clientId);
-            bool areAllPlayersConnected = m_connectedPlayerIds.Count >= m_expectedPlayerCount; // The game will begin at this point, or else there's a timeout for booting any unconnected players.
+            bool areAllPlayersConnected = NetworkManager.ConnectedClients.Count >= m_expectedPlayerCount; // The game will begin at this point, or else there's a timeout for booting any unconnected players.
             VerifyConnectionConfirm_ClientRpc(clientId, areAllPlayersConnected);
         }
         [ClientRpc]

Assets/Scripts/Game/InGame/SetupInGame.cs

 
         private bool m_isHost;
         private bool m_doesNeedCleanup = false;
+        private bool m_hasConnectedViaNGO = false;
 
         // TEMP? Relay stuff
         private ServerAddress m_serverAddress;
          * --- Need to make RelayUtpClient not an MB so I can freely disable the menus? It is on the GameManager, as it happens, but...
          * x Spawn the object with the NetworkManager and allow that to connect.
          * - Wait for all players to connect, or boot a player after a few seconds (via Relay) if they did not connect.
-         * - While waiting, server selects the target sequence, spawns the symbol container, and starts pooling/spawning the symbol objects.
+         * x While waiting, server selects the target sequence, spawns the symbol container, and starts pooling/spawning the symbol objects.
          * - Once all players are in, show the target sequence and instructions, and then the server starts moving the symbol container and listening to click events.
          * - After the symbols are all passed (I guess tracking the symbol container position or a timeout), finish the game (set the winner flag).
          * x Clients clean up and return to the lobby screen. Host sets the lobby back to the regular state.
 
         private void OnConnectionVerified()
         {
-            // TODO: Anything here?
+            m_hasConnectedViaNGO = true;
         }
 
         public void SetRelayAddress(LocalLobby changed)
 
             else if (type == MessageType.GameBeginning)
             {
-                // If this player hasn't successfully connected via NGO, get booted.
-                Locator.Get.Messenger.OnReceiveMessage(MessageType.DisplayErrorPopup, "Failed to join the game.");
-                // TODO: Need to handle both failing to connect and connecting but failing to initialize.
-                // I.e. cleaning up networked objects *might* be necessary.
+                if (!m_hasConnectedViaNGO)
+                {
+                    // If this player hasn't successfully connected via NGO, get booted.
+                    Locator.Get.Messenger.OnReceiveMessage(MessageType.DisplayErrorPopup, "Failed to join the game.");
+                    // TODO: Need to handle both failing to connect and connecting but failing to initialize.
+                    // I.e. cleaning up networked objects *might* be necessary.
+                }
             }
 
             else if (type == MessageType.ChangeGameState)