I have the same issue. Even when I go directly to the WindowsSignin.aspx URL it sends me to the login screen. I have full trust and it's in my trusted sites, although it's NOT in classic mode because, as you said, it wont work with the site in classic mode.
I think it's worth noting that, when I disabled Anonymous Authentication and enabled Windows Authentication on WindowsSignin.aspx, it shows an alert that says, "Challenge-based and login redirected-based authentication cannot be used simultaneously." I figured htis is because forms Authentication is enabled, but it says that feature "has been locked and is read only". This may not be an issue since the directory has it's own web.config which seems to have a location tag to disable it.
I did find an interesting writeup on IIS7:
In Integrated mode, ASP.NET modules will receive the first unauthenticated request to IIS when Anonymous authentication is disabled
In Integrated mode, when an IIS authentication scheme other then Anonymous authentication is used, the first request from the client that does not contain the required credentials will be visible to ASP.NET modules in the BeginRequest and AuthenticateRequest stages. In comparison, in Classic mode an ASP.NET application would not see such a request because it is rejected by IIS with a 401 challenge before ASP.NET has a chance to process it.
This means that ASP.NET modules will see an extra request in the BeginRequest and AuthenticateRequest stages. The request will appear in Web events and in any custom logging done in BeginRequest or EndRequest.