The following has worked for me in the past:
It allows you to convert any object to an Expando object.

public static dynamic ToDynamic<T>(this T obj)
{
    IDictionary<string, object> expando = new ExpandoObject();

    foreach (var propertyInfo in typeof(T).GetProperties())
    {
        var currentValue = propertyInfo.GetValue(obj);
        expando.Add(propertyInfo.Name, currentValue);
    }
    return expando as ExpandoObject;
}

Based on: http://geekswithblogs.net/Nettuce/archive/2012/06/02/convert-dynamic-to-type-and-convert-type-to-dynamic.aspx

As my object has JSON specific naming, I came up with this as an alternative:

public static dynamic ToDynamic(this object obj)
{
  var json = JsonConvert.SerializeObject(obj);
  return JsonConvert.DeserializeObject(json, typeof(ExpandoObject));
}

For me the results worked great:

Model:

public partial class Settings
{
  [JsonProperty("id")]
  public int Id { get; set; }

  [JsonProperty("runTime")]
  public TimeSpan RunTime { get; set; }

  [JsonProperty("retryInterval")]
  public TimeSpan RetryInterval { get; set; }

  [JsonProperty("retryCutoffTime")]
  public TimeSpan RetryCutoffTime { get; set; }

  [JsonProperty("cjisUrl")]
  public string CjisUrl { get; set; }

  [JsonProperty("cjisUserName")]
  public string CjisUserName { get; set; }

  [JsonIgnore]
  public string CjisPassword { get; set; }

  [JsonProperty("importDirectory")]
  public string ImportDirectory { get; set; }

  [JsonProperty("exportDirectory")]
  public string ExportDirectory { get; set; }

  [JsonProperty("exportFilename")]
  public string ExportFilename { get; set; }

  [JsonProperty("jMShareDirectory")]
  public string JMShareDirectory { get; set; }

  [JsonIgnore]
  public string Database { get; set; }
}

I used it in this manner:

private static dynamic DynamicSettings(Settings settings)
{
  var settingsDyn = settings.ToDynamic();
  if (settingsDyn == null)
    return settings;
  settingsDyn.guid = Guid.NewGuid();
  return settingsDyn;
}

And received this as a result:

{
  "id": 1,
  "runTime": "07:00:00",
  "retryInterval": "00:05:00",
  "retryCutoffTime": "09:00:00",
  "cjisUrl": "xxxxxx",
  "cjisUserName": "xxxxx",
  "importDirectory": "import",
  "exportDirectory": "output",
  "exportFilename": "xxxx.xml",
  "jMShareDirectory": "xxxxxxxx",
  "guid": "210d936e-4b93-43dc-9866-4bbad4abd7e7"
}

I don't know about speed, I mean it is serializing and deserializing, but for my use it has been great. A lot of flexability like hiding properties with JsonIgnore.

Note: xxxxx above is redaction. :)

You cannot add members to class instances on the fly.

But you can use ExpandoObject. Use factory to create new one and initialize it with properties which you have in MyClass:

public static ExpandoObject Create(int id)
{
    dynamic obj = new ExpandoObject();
    obj.Id = id;
    obj.CreatedAt = DateTime.Now;
    // etc
    return obj;
} 

Then you can add new members:

dynamic dto = Factory.Create(id);
dto.newProperty = "123";