WebAPI Routes not being recognized on Azure

I'm trying to deploy a WebAPI project to Azure.

It works locally. When I Publish it to Azure, I get 404 on the controller routes.

Looking at the logs, I see the routes are being handled as static files, instead of going through my controllers.

Module IIS Web Core Notification MapRequestHandler Handler StaticFile Error Code 0x80070002 Requested URL http://xxxxx:80/api/studies Physical Path D:\home\site\wwwroot\api\studies Logon Method Anonymous Logon User Anonymous

My Global.asax is:

    protected void Application_Start()
    {
        GlobalConfiguration.Configure(WebApiConfig.Register);
    }

And my WebApiConfig.Register is:

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

I've looked at similar questions and tried tweaking my Web.config to no avail. It currently looks like this (relevant part only):

<system.webServer>
    <httpErrors existingResponse="PassThrough"/>
    <validation validateIntegratedModeConfiguration="false" />
    <modules runAllManagedModulesForAllRequests="true">
    </modules>
    <handlers>
      <remove name="ExtensionlessUrlHandler-Integrated-4.0" />
      <remove name="OPTIONSVerbHandler" />
      <remove name="TRACEVerbHandler" />
      <add name="ExtensionlessUrlHandler-Integrated-4.0" path="*." verb="*" type="System.Web.Handlers.TransferRequestHandler" resourceType="Unspecified" requireAccess="Script" preCondition="integratedMode,runtimeVersionv4.0" />
    </handlers>
 </system.webServer>

By the way, I'm on Entity Framework 6 and not using MVC, just straight up WebAPI.

Somehow my Global.asax got excluded from the project, so the route mapping never happened.