I actually like a bit of ring. If i'm honest TS i used to be just like you when i first started having an interest in drums. I thought "oh i hate it when snares ring" but then i realised that the ring is half the point of the snare drum sound! The other thing is that you would probably find that if you listened to most of the recordings of your "ideal" snare drum sound without any of the other instruments then it would be a ringy sound because without that when the other instruments are mixed in you end up with that cardboard box sound that you said. So yeah that's what i like.