Web API Put Request genera un método Http 405 Error no permitido

Aquí está la llamada al método PUT en mi Web API - la tercera línea en el método (estoy llamando a la Web API desde un ASP.NET MVC front end):

client.BaseAddress is http://localhost/CallCOPAPI/.

Aquí está contactUri:

Aquí está contactUri.PathAndQuery:

Y finalmente, aquí está mi respuesta 405:

Aquí está la WebAPI.configuración en mi proyecto Web API:

        public static void Register(HttpConfiguration config)
        {
            config.Routes.MapHttpRoute(
                name: "DefaultApi",
                routeTemplate: "api/{controller}/{id}",
                defaults: new { id = RouteParameter.Optional }
            );

            config.Routes.MapHttpRoute(
                name: "DefaultApiGet",
                routeTemplate: "api/{controller}/{action}/{regionId}",
                defaults: new { action = "Get" },
                constraints: new { httpMethod = new HttpMethodConstraint("GET") });

            var json = config.Formatters.JsonFormatter;
            json.SerializerSettings.PreserveReferencesHandling = Newtonsoft.Json.PreserveReferencesHandling.Objects;
            config.Formatters.Remove(config.Formatters.XmlFormatter);

He intentado desnudar por el camino que se pasa en PutAsJsonAsync a string.Format("/api/department/{0}", department.Id) y string.Format("http://localhost/CallCOPAPI/api/department/{0}", department.Id) sin suerte.

¿Alguien tiene alguna idea de por qué estoy recibiendo el error 405?

UPDATE

Según la solicitud, aquí está mi código de controlador de Departamento (publicaré tanto el código de controlador de Departamento para mi proyecto front end, como el código de ApiController de Departamento para la WebAPI):

Front End Department Controller

namespace CallCOP.Controllers
{
    public class DepartmentController : Controller
    {
        HttpClient client = new HttpClient();
        HttpResponseMessage response = new HttpResponseMessage();
        Uri contactUri = null;

        public DepartmentController()
        {
            // set base address of WebAPI depending on your current environment
            client.BaseAddress = new Uri(ConfigurationManager.AppSettings[string.Format("APIEnvBaseAddress-{0}", CallCOP.Helpers.ConfigHelper.COPApplEnv)]);

            // Add an Accept header for JSON format.
            client.DefaultRequestHeaders.Accept.Add(
                new MediaTypeWithQualityHeaderValue("application/json"));
        }

        // need to only get departments that correspond to a Contact ID.
        // GET: /Department/?regionId={0}
        public ActionResult Index(int regionId)
        {
            response = client.GetAsync(string.Format("api/department/GetDeptsByRegionId/{0}", regionId)).Result;
            if (response.IsSuccessStatusCode)
            {
                var departments = response.Content.ReadAsAsync<IEnumerable<Department>>().Result;
                return View(departments);
            }
            else
            {
                LoggerHelper.GetLogger().InsertError(new Exception(string.Format(
                    "Cannot retrieve the list of department records due to HTTP Response Status Code not being successful: {0}", response.StatusCode)));
                return RedirectToAction("Index");
            }

        }

        //
        // GET: /Department/Create

        public ActionResult Create(int regionId)
        {
            return View();
        }

        //
        // POST: /Department/Create
        [HttpPost]
        [ValidateAntiForgeryToken]
        public ActionResult Create(int regionId, Department department)
        {
            department.RegionId = regionId;
            response = client.PostAsJsonAsync("api/department", department).Result;
            if (response.IsSuccessStatusCode)
            {
                return RedirectToAction("Edit", "Region", new { id = regionId });
            }
            else
            {
                LoggerHelper.GetLogger().InsertError(new Exception(string.Format(
                    "Cannot create a new department due to HTTP Response Status Code not being successful: {0}", response.StatusCode)));
                return RedirectToAction("Edit", "Region", new { id = regionId });
            }
        }

        //
        // GET: /Department/Edit/5

        public ActionResult Edit(int id = 0)
        {
            response = client.GetAsync(string.Format("api/department/{0}", id)).Result;
            Department department = response.Content.ReadAsAsync<Department>().Result;
            if (department == null)
            {
                return HttpNotFound();
            }
            return View(department);
        }

        //
        // POST: /Department/Edit/5

        [HttpPost]
        [ValidateAntiForgeryToken]
        public ActionResult Edit(int regionId, Department department)
        {
            response = client.GetAsync(string.Format("api/department/{0}", department.Id)).Result;
            contactUri = response.RequestMessage.RequestUri;
            response = client.PutAsJsonAsync(string.Format(contactUri.PathAndQuery), department).Result;
            if (response.IsSuccessStatusCode)
            {
                return RedirectToAction("Index", new { regionId = regionId });
            }
            else
            {
                LoggerHelper.GetLogger().InsertError(new Exception(string.Format(
                    "Cannot edit the department record due to HTTP Response Status Code not being successful: {0}", response.StatusCode)));
                return RedirectToAction("Index", new { regionId = regionId });
            }
        }

        //
        // GET: /Department/Delete/5

        public ActionResult Delete(int id = 0)
        {
            response = client.GetAsync(string.Format("api/department/{0}", id)).Result;
            Department department = response.Content.ReadAsAsync<Department>().Result;

            if (department == null)
            {
                return HttpNotFound();
            }
            return View(department);
        }

        //
        // POST: /Department/Delete/5

        [HttpPost, ActionName("Delete")]
        [ValidateAntiForgeryToken]
        public ActionResult DeleteConfirmed(int regionId, int id)
        {
            response = client.GetAsync(string.Format("api/department/{0}", id)).Result;
            contactUri = response.RequestMessage.RequestUri;
            response = client.DeleteAsync(contactUri).Result;
            return RedirectToAction("Index", new { regionId = regionId });
        }
    }
}

Departamento de API web ApiController

namespace CallCOPAPI.Controllers
{
    public class DepartmentController : ApiController
    {
        private CallCOPEntities db = new CallCOPEntities(HelperClasses.DBHelper.GetConnectionString());

        // GET api/department
        public IEnumerable<Department> Get()
        {
            return db.Departments.AsEnumerable();
        }

        // GET api/department/5
        public Department Get(int id)
        {
            Department dept = db.Departments.Find(id);
            if (dept == null)
            {
                throw new HttpResponseException(Request.CreateResponse(HttpStatusCode.NotFound));
            }

            return dept;
        }

        // this should accept a contact id and return departments related to the particular contact record
        // GET api/department/5
        public IEnumerable<Department> GetDeptsByRegionId(int regionId)
        {
            IEnumerable<Department> depts = (from i in db.Departments
                                             where i.RegionId == regionId 
                                             select i);
            return depts;
        }

        // POST api/department
        public HttpResponseMessage Post(Department department)
        {
            if (ModelState.IsValid)
            {
                db.Departments.Add(department);
                db.SaveChanges();

                HttpResponseMessage response = Request.CreateResponse(HttpStatusCode.Created, department);
                return response;
            }
            else
            {
                return Request.CreateErrorResponse(HttpStatusCode.BadRequest, ModelState);
            }
        }

        // PUT api/department/5
        public HttpResponseMessage Put(int id, Department department)
        {
            if (!ModelState.IsValid)
            {
                return Request.CreateErrorResponse(HttpStatusCode.BadRequest, ModelState);
            }

            if (id != department.Id)
            {
                return Request.CreateResponse(HttpStatusCode.BadRequest);
            }

            db.Entry(department).State = EntityState.Modified;

            try
            {
                db.SaveChanges();
            }
            catch (DbUpdateConcurrencyException ex)
            {
                return Request.CreateErrorResponse(HttpStatusCode.NotFound, ex);
            }

            return Request.CreateResponse(HttpStatusCode.OK);
        }

        // DELETE api/department/5
        public HttpResponseMessage Delete(int id)
        {
            Department department = db.Departments.Find(id);
            if (department == null)
            {
                return Request.CreateResponse(HttpStatusCode.NotFound);
            }

            db.Departments.Remove(department);

            try
            {
                db.SaveChanges();
            }
            catch (DbUpdateConcurrencyException ex)
            {
                return Request.CreateErrorResponse(HttpStatusCode.NotFound, ex);
            }

            return Request.CreateResponse(HttpStatusCode.OK, department);
        }
    }
}