I was able to avoid this (at least with interfaces) by inheriting from a separate class containing the nested interfaces. (In my scenario I am also returning references to these interfaces.)
Instead of:
public class MyClass<T1, T2, T3> :
   MyClass<T1, T2, T3>.Interface
where T1 : ...
where T2 : ... 
where T3 : ... {
   public interface Interface { Interface SomeMethod(); }
   Interface Interface.SomeMethod() {
      ...
   }
}
// compile error: Circular base class dependency
Do something like this:
public sealed class MyClassInterfaces<T1, T2, T3>
where T1 : ...
where T2 : ... 
where T3 : ... {
   public interface Interface { Interface SomeMethod(); }
}
sealed class MyClass<T1, T2, T3> :
   MyClassInterfaces<T1, T2, T3>.Interface
where T1 : ...
where T2 : ... 
where T3 : ... {
   MyClassInterfaces<T1, T2, T3>.Interface
   MyClassInterfaces<T1, T2, T3>.Interface.SomeMethod() {
      ...
   }
}
To avoid the ugliness with explicit interface implementations, you can also inherit from the other class, though that wouldn't work if you were trying to inherit from a nested class, since you can't inherit from both classes.
public abstract class MyClassInterfaces<T1, T2, T3>
where T1 : ...
where T2 : ... 
where T3 : ... {
   public interface Interface { Interface SomeMethod(); }
}
sealed class MyClass<T1, T2, T3> :
   MyClassInterfaces<T1, T2, T3>,
   MyClassInterfaces<T1, T2, T3>.Interface
where T1 : ...
where T2 : ... 
where T3 : ... {
   Interface Interface.SomeMethod() {
      ...
   }
}