A really hacky way to grab the HttpContext from the request of a WCF Web API DelegatingHandler...

HttpRequestMessageExtensions.cs

using System;
using System.Net;
using System.Net.Http;
using System.Reflection;
using System.ServiceModel;
using System.Text;
using System.Threading;
using System.Threading.Tasks;
using System.Web;

namespace Ugh {

public static class HttpRequestMessageExtensions
{
    static FieldInfo _currentThreadDataField;
    static FieldInfo _httpContextField;

    public static HttpContext GetHttpContext(this HttpRequestMessage request)
    {
        var webHost = request.Properties["webhost"];

        if (webHost==null) throw new Exception("Request does not contain webHost property");

        if (_currentThreadDataField == null)
        {
            _currentThreadDataField = webHost.GetType().GetField("currentThreadData", BindingFlags.NonPublic | BindingFlags.Instance);

            if (_currentThreadDataField == null)
            {
                throw new Exception("webHost does not contain currentThreadData field");
            }
        }

        var currentThreadData = _currentThreadDataField.GetValue(webHost);

        if (_httpContextField == null)
        {
            _httpContextField = currentThreadData.GetType().GetField("httpContext", BindingFlags.NonPublic | BindingFlags.Instance);

            if (_httpContextField == null)
            {
                throw new Exception("currentThreadData does not contain httpContext field");
            }
        }

        return (HttpContext)_httpContextField.GetValue(currentThreadData);            
    }
}

}