Try adding it to the collection instead of overriding the DefaultHandler. The following worked for me on version 1.1.2:
public void Configure(IApplicationBuilder app, IHostingEnvironment env, ILoggerFactory loggerFactory)
{
    // ... other configuration
    app.UseMvc(routes =>
    {
        routes.Routes.Add(new HostPropagationRouter(routes.DefaultHandler));
        routes.MapRoute(
            name: "default",
            template: "{controller=Home}/{action=Index}/{id?}");
    });
    // ... other configuration
}
Here's the router, just for completeness.
public class HostPropagationRouter : IRouter
{
    readonly IRouter router;
    public HostPropagationRouter(IRouter router)
    {
        this.router = router;
    }
    public VirtualPathData GetVirtualPath(VirtualPathContext context)
    {
        if (context.HttpContext.Request.Query.TryGetValue("host", out var host))
            context.Values["host"] = host;
        return router.GetVirtualPath(context);
    }
    public Task RouteAsync(RouteContext context) => router.RouteAsync(context);
}