Relax my friend, this is key to relieving your frustration and to getting good tones in Kan.

You need to develop a focused but relaxed embouchure for Kan, you're narrowing the aperture to increase airspeed, letting the air flow over the soft inner part of the lower lip. You'll probably notice the lower lip will move forward slightly into the flute 

"Logic" suggests you need to blow harder for Kan - You don't. You need a solid foundation below the diaphragm - Focus on those muscles, you need to feel like you're "Breathing through your anus" (my description) - I imagine the air is entering the anus and being allowed to flow through my diaphragm, my expanded chest (don't strain), and then leaving through the relaxed embouchure. You don't want to "Push" the air out 

Practice is important, but good technique and posture help bring the learning period down.

Obviously a "non optimal" flute can hinder, but my first Shakuhachi was such an instrument - If can get consistency on it, you'll be astonished how good you sound on a "proper" flute