Inherit from HttpWebRequest... pure evil will ensue.

MyHttpWebRequest.cs

public class MyHttpWebRequest : HttpWebRequest
    {
        private static readonly IFormatterConverter Converter = new FormatterConverter();
        private static readonly StreamingContext Context = new StreamingContext(StreamingContextStates.Clone);
 
        public MyHttpWebRequest(string url)
            : this(new Uri(url))
        {
        }
 
        public MyHttpWebRequest(Uri uri)
            : this(CreateHttpWebRequestSerializationInfo(uri), Context)
        {
        }
 
        protected MyHttpWebRequest(SerializationInfo serializationInfo, StreamingContext streamingContext)
            : base(serializationInfo, streamingContext)
        {
        }
 
        private static SerializationInfo CreateHttpWebRequestSerializationInfo(Uri uri)
        {
            var httpWebRequest = WebRequest.CreateDefault(uri) as ISerializable;
            {
                var serializationInfo = new SerializationInfo(typeof(HttpWebRequest), Converter);
                httpWebRequest.GetObjectData(serializationInfo, Context);
                return serializationInfo;
            }
        }
    }

This doesn't work out of the box. After instantiating the class you need a bit of reflection to set the _Url field. It looks like at some point they added _Url and serialized version only sets _OrigUrl.