This will copy UnityEvents from one UnityEvent to Another. It should copy all the settings exactly as is. Tested on Unity2018.4

CopyUnityEvents.cs

public static void CopyUnityEvents(object sourceObj, string source_UnityEvent, object dest, bool debug = false)
{
    FieldInfo unityEvent = sourceObj.GetType().GetField(source_UnityEvent, E_Helpers.allBindings);
    if (unityEvent.FieldType != dest.GetType())
    {
        if (debug == true)
        {
            Debug.Log("Source Type: " + unityEvent.FieldType);
            Debug.Log("Dest Type: " + dest.GetType());
            Debug.Log("CopyUnityEvents - Source & Dest types don't match, exiting.");
        }
        return;
    }
    else
    {
        SerializedObject so = new SerializedObject((Object)sourceObj);
        SerializedProperty persistentCalls = so.FindProperty(source_UnityEvent).FindPropertyRelative("m_PersistentCalls.m_Calls");
        for (int i = 0; i < persistentCalls.arraySize; ++i)
        {
            Object target = persistentCalls.GetArrayElementAtIndex(i).FindPropertyRelative("m_Target").objectReferenceValue;
            string methodName = persistentCalls.GetArrayElementAtIndex(i).FindPropertyRelative("m_MethodName").stringValue;
            MethodInfo method = null;
            try
            {
                method = target.GetType().GetMethod(methodName, E_Helpers.allBindings);
            }
            catch
            {
                foreach (MethodInfo info in target.GetType().GetMethods(E_Helpers.allBindings).Where(x => x.Name == methodName))
                {
                    ParameterInfo[] _params = info.GetParameters();
                    if (_params.Length < 2)
                    {
                        method = info;
                    }
                }
            }
            ParameterInfo[] parameters = method.GetParameters();
            switch(parameters[0].ParameterType.Name)
            {
                case nameof(System.Boolean):
                    bool bool_value = persistentCalls.GetArrayElementAtIndex(i).FindPropertyRelative("m_Arguments.m_BoolArgument").boolValue;
                    var bool_execute = System.Delegate.CreateDelegate(typeof(UnityAction<bool>), target, methodName) as UnityAction<bool>;
                    UnityEventTools.AddBoolPersistentListener(
                        dest as UnityEventBase,
                        bool_execute,
                        bool_value
                    );
                    break;
                case nameof(System.Int32):
                    int int_value = persistentCalls.GetArrayElementAtIndex(i).FindPropertyRelative("m_Arguments.m_IntArgument").intValue;
                    var int_execute = System.Delegate.CreateDelegate(typeof(UnityAction<int>), target, methodName) as UnityAction<int>;
                    UnityEventTools.AddIntPersistentListener(
                        dest as UnityEventBase,
                        int_execute,
                        int_value
                    );
                    break;
                case nameof(System.Single):
                    float float_value = persistentCalls.GetArrayElementAtIndex(i).FindPropertyRelative("m_Arguments.m_FloatArgument").floatValue;
                    var float_execute = System.Delegate.CreateDelegate(typeof(UnityAction<float>), target, methodName) as UnityAction<float>;
                    UnityEventTools.AddFloatPersistentListener(
                        dest as UnityEventBase,
                        float_execute,
                        float_value
                    );
                    break;
                case nameof(System.String):
                    string str_value = persistentCalls.GetArrayElementAtIndex(i).FindPropertyRelative("m_Arguments.m_StringArgument").stringValue;
                    var str_execute = System.Delegate.CreateDelegate(typeof(UnityAction<string>), target, methodName) as UnityAction<string>;
                    UnityEventTools.AddStringPersistentListener(
                        dest as UnityEventBase,
                        str_execute,
                        str_value
                    );
                    break;
                case nameof(System.Object):
                    Object obj_value = persistentCalls.GetArrayElementAtIndex(i).FindPropertyRelative("m_Arguments.m_ObjectArgument").objectReferenceValue;
                    var obj_execute = System.Delegate.CreateDelegate(typeof(UnityAction<Object>), target, methodName) as UnityAction<Object>;
                    UnityEventTools.AddObjectPersistentListener(
                        dest as UnityEventBase,
                        obj_execute,
                        obj_value
                    );
                    break;
                default:
                    var void_execute = System.Delegate.CreateDelegate(typeof(UnityAction), target, methodName) as UnityAction;
                    UnityEventTools.AddPersistentListener(
                        dest as UnityEvent,
                        void_execute
                    );
                    break;
            }
        }
    }
}

The issue with removing the old calls came about when the source and destination were equal. Hence, this is the modification:

if (!dryRun)
{
    if (removeOldCalls && (dstCalls.arraySize > 0))
    {
        srcCalls.ClearArray();
    }
    src.ApplyModifiedProperties();
    if (source != destination)
    {
        dst.ApplyModifiedProperties();
    }
}