Question Trouble with EditorGUI.Popup updating

I am attempting to create a custom property drawer for Unity object references that eliminates the need to drag and drop component references. The idea is that the property will be split into a standard field for the object reference and a popup from which the user can select an object reference, like so:



I am running into issues updating both the dropdown and the property correctly. Here is my OnGUI method:

Code (CSharp):

1. public override void OnGUI(Rect position, SerializedProperty property, GUIContent label)
2.         {
3.             var list = Objects(property, GetAttribute.GetterSource);
4.            
5.             EditorGUI.BeginProperty(position, label, property);
6.  
7.             if (list.Length <= 0)
8.             {
9.                 // Handle this case. Not important.
10.             }
11.  
12.             var listNames = AsNames(list).ToArray(); // Converts the names to strings. This does not affect the contents of list.
13.  
14.             EditorGUI.BeginChangeCheck();
15.             _index = EditorGUI.Popup(RightSide(position), _index, listNames); // _index is a private int. LeftSide and RightSide return the left and right halves of the Rect parameter.
16.            
17.             if (EditorGUI.EndChangeCheck())
18.             {
19.                 Undo.RecordObject(property.serializedObject.targetObject, $"Set index to {_index}");
20.                 property.serializedObject.Update();
21.                 property.objectReferenceValue = list[_index];
22.             }
23.  
24.             GUI.enabled = false;
25.             GUI.backgroundColor = property.objectReferenceValue == null ? Color.red : Color.white;
26.            
27.             EditorGUI.PropertyField(LeftSide(position), property, new GUIContent(GetterLabel(label)));
28.             property.serializedObject.ApplyModifiedProperties();
29.  
30.             EditorGUI.EndProperty();
31.         }

As it stands now, the object reference updates accurately, but the popup does not.

Moving

property.serializedObject.Update();

down one line--that is, after

property.objectReferenceValue

is updated--makes the popup update accurately, but prevents the object reference from updating at all.

I am very new to editor scripting, so I would appreciate it immensely if you would point out my mistakes!

If you are interested in testing the full code, you can find it here: Buggy PropertyDrawer - Pastebin.com

Thank you so, so much in advance!