Unity IoC, resolve constructor dependency by it's context

Question

I'm trying to register multiple implementation of single interface, but I would like to avoid using named type registration. Let's say I'm having following code:

public interface IStorage { ... }
public class DocumentStorage : IStorage { ... }
public class ImageStorage : IStorage { ... }

public interface IRepository { ... }
public class DocumentRepository : IRepository
{
    public DocumentRepository(IStorage storage /*, ... and other dependencies */) { ... }
}

And doing all Unity IoC registration on single file. Rest of application does not have access to container (+ service locator pattern is big no no in my code)

Registering this would then look like this:

container.RegisterType<IStorage, DocumentStorage>("document");
container.RegisterType<IStorage, ImageStorage>("image");

container.RegisterType<IRepository, DocumentRepository>(
    new InjectionFactory((c, t, s) => new DocumentRepository(
        c.Resolve<IStorage>("document") /*, ... resolve other deps here */)));

And here is lying my laziness issue - I really don't want to write resolution of all dependencies this way - this makes IoC hassle. I would have to go trough all registrations depending on one of IStorage implementations and resolve all other dependencies manually.

I was thinking of turned-around solution by registering DocumentStorage resolved by DocumentRepository - which I'm not able to figure out, and moreover, it is putting dependency on another side of "equation" ("register type for being injected to another type" (instead of "register type and let it be resolved if something depends on it")).

Is there any other way how to make registration easier? (I'm not focusing on factory here - I could imagine other non-factory-able usages requiring similar way of registering dependencies)

Thanks for any advice :)