How does one log the full HTTP request and response when running integration tests of an ASP.NET MVC 3 application? - c#-4.0

Question

Assume I have a ASP.NET MVC 3 controller and action for which I'd wrote integration tests.
namespace Sample.Controllers {
public class MyController : Controller {
[HttpPost]
public ActionResult Edit(MyModel model)
{
// process requests
}
}
}
The tests have the following "pattern".
namespace Sample.Controllers.IntegrationTests {
[TestClass]
public class MyControllerTests
{
[TestMethod]
public void Edit()
{
var request = (HttpWebRequest) WebRequest.Create(new Uri(uri));
request.Method = "POST";
request.Accept = "application/json";
request.AllowAutoRedirect = false;
request.AutomaticDecompression = DecompressionMethods.GZip;
request.UserAgent = "IntegrationTests/1.0";
request.ContentType = "application/json";
var resource = CreateResource();
using (Stream stream = request.GetRequestStream())
{
// serialize resource to stream
}
using (var response = (HttpWebResponse) request.GetResponse())
{
Assert.AreEqual(HttpStatusCode.OK, response.StatusCode);
/* perform more tests */
}
}
public MyModel CreateResource() {
/* create an instance of mymodel */
}
}
}
These tests aim to verify functionally, security and so forth; so mocking and unit tests don't suffice. The tests are executed in an unattended fashion and always uses https (and certs are verified for security reasons), so using a proxy is problematic. They are also executed with limited privileges.
Every now and then tests fail. I'd like to save a copy of the request and response (similar to what fiddler does) and associate it with each test, so that one can retrospectively use it to diagnose problems, if any exists.
Can one save the request and responses (incl. their headers) to disk without side effects that change the outcome of the tests? For example, for large streams, the response stream isn't seekable, so attempting to save the stream to disk before continuing to test the response doesn't seem to work.