Ninject InSingletonScope with Web Api RC

I'm having some difficulty using Ninject's InSingletonScope binding with Web Api RC. No matter how I create my binding, it looks like perhaps Web Api is handling scope/lifetime instead of Ninject.

I've tried a few variations on wiring up Ninject. The most common is identical to the answer here:
ASP.NET Web API binding with ninject

I've also tried this version:
http://www.peterprovost.org/blog/2012/06/19/adding-ninject-to-web-api/

In both, I'm literally creating an out of the box Web Api project, then adding the Ninject packages as described in either post. Finally, I'm adding the Resolver and Scope classes, such as this for the StackOverflow version:

public class NinjectDependencyScope : IDependencyScope
{
    private IResolutionRoot resolver;

    internal NinjectDependencyScope(IResolutionRoot resolver)
    {
        Contract.Assert(resolver != null);

        this.resolver = resolver;
    }

    public void Dispose()
    {
        IDisposable disposable = resolver as IDisposable;
        if (disposable != null)
            disposable.Dispose();

        resolver = null;
    }
    public object GetService(Type serviceType)
    {
        if (resolver == null)
            throw new ObjectDisposedException("this", "This scope has already been disposed");
        return resolver.TryGet(serviceType);
    }

    public IEnumerable<object> GetServices(Type serviceType)
    {
        if (resolver == null)
            throw new ObjectDisposedException("this", "This scope has already been disposed");
        return resolver.GetAll(serviceType);
    }
}

and:

 public class NinjectDependencyResolver : NinjectDependencyScope, IDependencyResolver
{
    private IKernel kernel;

    public NinjectDependencyResolver(IKernel kernel)
        : base(kernel)
    {
        this.kernel = kernel;
    }
    public IDependencyScope BeginScope()
    {
        return new NinjectDependencyScope(kernel.BeginBlock());
    }
}

Then, NinjectWebCommon looks like this:

using System.Web.Http;
using MvcApplication2.Controllers;

[assembly: WebActivator.PreApplicationStartMethod(typeof(MvcApplication2.App_Start.NinjectWebCommon), "Start")]
[assembly: WebActivator.ApplicationShutdownMethodAttribute(typeof(MvcApplication2.App_Start.NinjectWebCommon), "Stop")]

namespace MvcApplication2.App_Start
{
    using System;
    using System.Web;

    using Microsoft.Web.Infrastructure.DynamicModuleHelper;

    using Ninject;
    using Ninject.Web.Common;

    public static class NinjectWebCommon
    {
        private static readonly Bootstrapper bootstrapper = new Bootstrapper();

        /// <summary>
        /// Starts the application
        /// </summary>
        public static void Start()
        {
            DynamicModuleUtility.RegisterModule(typeof(OnePerRequestHttpModule));
            DynamicModuleUtility.RegisterModule(typeof(NinjectHttpModule));
            bootstrapper.Initialize(CreateKernel);
        }

        /// <summary>
        /// Stops the application.
        /// </summary>
        public static void Stop()
        {
            bootstrapper.ShutDown();
        }

        /// <summary>
        /// Creates the kernel that will manage your application.
        /// </summary>
        /// <returns>The created kernel.</returns>
        private static IKernel CreateKernel()
        {
            var kernel = new StandardKernel();
            kernel.Bind<Func<IKernel>>().ToMethod(ctx => () => new Bootstrapper().Kernel);
            kernel.Bind<IHttpModule>().To<HttpApplicationInitializationHttpModule>();

            // Register Dependencies
            RegisterServices(kernel);

            // Set Web API Resolver
            GlobalConfiguration.Configuration.DependencyResolver = new NinjectDependencyResolver(kernel);

            return kernel;
        }

        /// <summary>
        /// Load your modules or register your services here!
        /// </summary>
        /// <param name="kernel">The kernel.</param>
        private static void RegisterServices(IKernel kernel)
        {
            kernel.Bind<ILogger>().To<Logger>().InSingletonScope();
        }
    }
}

The ILogger and Logger objects don't do anything, but illustrate the issue. Logger does Debug.Writeline so that I can see when it was instantiated. And each refresh of the page shows that it's being refreshed per call, rather than the singleton I'd hoped for. Here is a controller using the Logger:

public class ValuesController : ApiController
{
    private readonly ILogger _logger;
    public ValuesController(ILogger logger)
    {
        _logger = logger;
        _logger.Log("Logger created at " + System.DateTime.Now.ToLongTimeString());
    }
    // GET api/values
    public IEnumerable<string> Get()
    {
        return new string[] { "value1", "value2" };
    }
    // GET api/values/5
    public string Get(int id)
    {
        return "value";
    }
    // POST api/values
    public void Post(string value)
    {
    }
    // PUT api/values/5
    public void Put(int id, string value)
    {
    }
    // DELETE api/values/5
    public void Delete(int id)
    {
    }
}

When I put trace information into the creation of the kernel, it seems to show that the kernel is only created once. So… what am I not seeing? Why isn't the singleton persisted?