How to get hold of Content that is already read

Don't include the body parameter in the signature and that will allow you to buffer the content and read the content as many times as you like.

[PUT("user/{UserId}")]
public HttpResponseMessage Put(string userId)
{
    Request.Content.LoadIntoBufferAsync().Wait();
    var paymentRequest = Request.Content.ReadAsAsync<PaymentRequest>().Result;
    var requestBody = Request.Content.ReadAsStringAsync().Result;
    // Calling business logic and so forth here
    // Return proper HttpResponseMessage here
}

You could read from the underlying request:

using (var stream = new MemoryStream())
{
    var context = (HttpContextBase)Request.Properties["MS_HttpContext"];
    context.Request.InputStream.Seek(0, SeekOrigin.Begin);
    context.Request.InputStream.CopyTo(stream);
    string requestBody = Encoding.UTF8.GetString(stream.ToArray());
}