I agree, as well. As you go higher, you’ll need to narrow the gap you’re not covering with the thumb (experiment a bit to get the right thumb placement). I found it easier after I cut and filed my left thumbnail very, very short. In addition to increasing your breath pressure, you might experiment with narrowing/focusing the airstream, as well (i.e., colder/faster air as you go higher). I’ve gradually improved at hitting the notes in the second register. I can go up to a high E, currently. Still working on doing that consistently, though.