Do you ever think you are playing pretty well and you can actually feel the whistle vibrating under your fingers like it’s alive?
This happens with my brass Burke sometimes. I think it’s because I’m no longer gripping too hard and my finger are finally fluttering like I’ve been practicing - that’s taken months I don’t mind saying.
I don’t play any other high Ds and my low D vibrates because it’s basically a drain pipe with a lower frequency.
Gripping too hard is still my main problem. It causes a bit of pain in that joint where the thumb and index finger join together. If I don’t do that, though, I can’t keep the holes covered and my low D squeeks and squawks. I think I’m just going to have to keep practising and maybe, like you, after a few more months I’ll get better. 
Covering the holes is the big issue when you start. It comes with practice and obviously it is crucial. It helps if you aren’t covering the holes with the very tippy tips of your fingers like on a recorder, but using the pads of the last part of your fingers which cover the holes better.
Good luck. If it helps, I’ve been playing a while but I’m never happy with what I’ve achieved. Actually, that doesn’t help does it?
edit to say the low D is the biggest culprit in the battle to cover the holes, because they are so big and far spaced.
You could phrase it like you’re always striving for perfection. That would sound a bit better. 
Indeed I look for that quality in every instrument I play. Having spent most of my life playing instruments made of wood, it’s interesting to me that even a length of brass or delrin can feel alive under your fingers, provided you’re putting your heart and soul into it!
…when all the animals in the neighbourhood DON’T evacuate to the surrounding hills when you start to play 