System.Net.WebException

My suggestion would be to use RestSharp. You can make calls to REST services and have them cast into POCO objects with very little boilerplate code to actually have to parse through the response. This will not solve your particular error, but it answers your overall question of how to make calls to REST services. Having to change your code to use it should pay off in the ease of use and robustness moving forward. That is just my two cents though.

Example:

namespace RestSharpThingy
{
    using System;
    using System.Collections.Generic;
    using System.IO;
    using System.Linq;
    using System.Net;
    using System.Reflection;
    using RestSharp;

    public static class Program
    {
        public static void Main()
        {
            Uri baseUrl = new Uri("https://httpbin.org/");
            IRestClient client = new RestClient(baseUrl);
            IRestRequest request = new RestRequest("get", Method.GET) { Credentials = new NetworkCredential("testUser", "P455w0rd") };

            request.AddHeader("Authorization", "Bearer qaPmk9Vw8o7r7UOiX-3b-8Z_6r3w0Iu2pecwJ3x7CngjPp2fN3c61Q_5VU3y0rc-vPpkTKuaOI2eRs3bMyA5ucKKzY1thMFoM0wjnReEYeMGyq3JfZ-OIko1if3NmIj79ZSpNotLL2734ts2jGBjw8-uUgKet7jQAaq-qf5aIDwzUo0bnGosEj_UkFxiJKXPPlF2L4iNJSlBqRYrhw08RK1SzB4tf18Airb80WVy1Kewx2NGq5zCC-SCzvJW-mlOtjIDBAQ5intqaRkwRaSyjJ_MagxJF_CLc4BNUYC3hC2ejQDoTE6HYMWMcg0mbyWghMFpOw3gqyfAGjr6LPJcIly__aJ5__iyt-BTkOnMpDAZLTjzx4qDHMPWeND-TlzKWXjVb5yMv5Q6Jg6UmETWbuxyTdvGTJFzanUg1HWzPr7gSs6GLEv9VDTMiC8a5sNcGyLcHBIJo8mErrZrIssHvbT8ZUPWtyJaujKvdgazqsrad9CO3iRsZWQJ3lpvdQwucCsyjoRVoj_mXYhz3JK3wfOjLff16Gy1NLbj4gmOhBBRb8rJnUXnP7rBHs00FAk59BIpKLIPIyMgYBApDCut8V55AgXtGs4MgFFiJKbuaKxq8cdMYEVBTzDJ-S1IR5d6eiTGusD5aFlUkAs9NV_nFw");
            request.AddParameter("clientId", 123);

            IRestResponse<RootObject> response = client.Execute<RootObject>(request);

            if (response.IsSuccessful)
            {
                response.Data.Write();
            }
            else
            {
                Console.WriteLine(response.ErrorMessage);
            }

            Console.WriteLine();

            string path = Assembly.GetExecutingAssembly().Location;
            string name = Path.GetFileName(path);

            request = new RestRequest("post", Method.POST);
            request.AddFile(name, File.ReadAllBytes(path), name, "application/octet-stream");
            response = client.Execute<RootObject>(request);
            if (response.IsSuccessful)
            {
                response.Data.Write();
            }
            else
            {
                Console.WriteLine(response.ErrorMessage);
            }

            Console.ReadLine();
        }

        private static void Write(this RootObject rootObject)
        {
            Console.WriteLine("clientId: " + rootObject.args.clientId);
            Console.WriteLine("Accept: " + rootObject.headers.Accept);
            Console.WriteLine("AcceptEncoding: " + rootObject.headers.AcceptEncoding);
            Console.WriteLine("AcceptLanguage: " + rootObject.headers.AcceptLanguage);
            Console.WriteLine("Authorization: " + rootObject.headers.Authorization);
            Console.WriteLine("Connection: " + rootObject.headers.Connection);
            Console.WriteLine("Dnt: " + rootObject.headers.Dnt);
            Console.WriteLine("Host: " + rootObject.headers.Host);
            Console.WriteLine("Origin: " + rootObject.headers.Origin);
            Console.WriteLine("Referer: " + rootObject.headers.Referer);
            Console.WriteLine("UserAgent: " + rootObject.headers.UserAgent);
            Console.WriteLine("origin: " + rootObject.origin);
            Console.WriteLine("url: " + rootObject.url);
            Console.WriteLine("data: " + rootObject.data);
            Console.WriteLine("files: ");
            foreach (KeyValuePair<string, string> kvp in rootObject.files ?? Enumerable.Empty<KeyValuePair<string, string>>())
            {
                Console.WriteLine("\t" + kvp.Key + ": " + kvp.Value);
            }
        }
    }

    public class Args
    {
        public string ClientId { get; set; }
    }

    public class Headers
    {
        public string Accept { get; set; }

        public string AcceptEncoding { get; set; }

        public string AcceptLanguage { get; set; }

        public string Authorization { get; set; }

        public string Connection { get; set; }

        public string Dnt { get; set; }

        public string Host { get; set; }

        public string Origin { get; set; }

        public string Referer { get; set; }

        public string UserAgent { get; set; }
    }

    public class RootObject
    {
        public Args args { get; set; }

        public Headers Headers { get; set; }

        public string Origin { get; set; }

        public string Url { get; set; }

        public string Data { get; set; }

        public Dictionary<string, string> Files { get; set; }
    }
}

Try setting maxReceivedMessageSize on the server too, e.g. to 4MB:

<binding name="MyService.MyServiceBinding" maxReceivedMessageSize="4194304">

The main reason the default (65535 I believe) is so low is to reduce the risk of Denial of Service (DoS) attacks. You need to set it bigger than the maximum request size on the server, and the maximum response size on the client. If you're in an Intranet environment, the risk of DoS attacks is probably low, so it's probably safe to use a value much higher than you expect to need.

By the way a couple of tips for troubleshooting problems connecting to WCF services:

• Enable tracing on the server as described in this MSDN article.

• Use an HTTP debugging tool such as Fiddler on the client to inspect the HTTP traffic.

Unrelated, I'm sure, but do wrap your IDisposable objects in using blocks to ensure proper disposal:

using System;
using System.Net;
using System.IO;

namespace ConsoleProgram
{
    public class Class1
    {
        private const string URL = "https://sub.domain.com/objects.json?api_key=123";
        private const string DATA = @"{""object"":{""name"":""Name""}}";

        static void Main(string[] args)
        {
            Class1.CreateObject();
        }

        private static void CreateObject()
        {
            HttpWebRequest request = (HttpWebRequest)WebRequest.Create(URL);
            request.Method = "POST";
            request.ContentType = "application/json";
            request.ContentLength = DATA.Length;
            using (Stream webStream = request.GetRequestStream())
            using (StreamWriter requestWriter = new StreamWriter(webStream, System.Text.Encoding.ASCII))
            {
                requestWriter.Write(DATA);
            }

            try
            {
                WebResponse webResponse = request.GetResponse();
                using (Stream webStream = webResponse.GetResponseStream() ?? Stream.Null)
                using (StreamReader responseReader = new StreamReader(webStream))
                {
                    string response = responseReader.ReadToEnd();
                    Console.Out.WriteLine(response);
                }
            }
            catch (Exception e)
            {
                Console.Out.WriteLine("-----------------");
                Console.Out.WriteLine(e.Message);
            }
        }
    }
}

Here are a few different ways of calling an external API in C# (updated 2019).

.NET's built-in ways:

• WebRequest& WebClient - verbose APIs & Microsoft's documentation is not very easy to follow
• HttpClient - .NET's newest kid on the block & much simpler to use than above.

Free, open-source NuGet Packages, which frankly have a much better developer experience than .NET's built in clients:

• ServiceStack.Text (1,000 GitHub stars, 7 million NuGet downloads) (*) - fast, light and resilient.
• RestSharp (6,000 GitHub stars, 23 million NuGet downloads) (*) - simple REST and HTTP API Client
• Flurl (1,700 GitHub stars, 3 million NuGet downloads) (*)- a fluent, portable, testable HTTP client library

All the above packages provide a great developer experience (i.e., concise, easy API) and are well maintained.

(*) as at August 2019

Example: Getting a Todo item from a Fake Rest API using ServiceStack.Text. The other libraries have very similar syntax.

class Program
{
    static void Main(string[] args)
    {
        // Fake rest API
        string url = "https://jsonplaceholder.typicode.com/todos/1";

        // GET data from API & map to POCO
        var todo =  url.GetJsonFromUrl().FromJson<Todo>();

        // Print the result to screen
        todo.PrintDump();
    }

    public class Todo
    {
        public int UserId { get; set; }
        public int Id { get; set; }
        public string Title { get; set; }
        public bool Completed { get; set; }
    }

}

Running the above example in a .NET Core Console app, produces the following output.

Install these packages using NuGet

Install-Package ServiceStack.Text, or

Install-Package RestSharp, or

Install-Package Flurl.Http