If you're stirrups feel too short than they probably are. I also am 1.7m tall and have found that holding the stirrup under my arm doesn't work at all for me. I generally use the rule that payette mentioned as it's pretty much fool proof for us long leggies! Haha
Looking at the picture the immediate problem is that your foot is jammed through the stirrup which has been mentioned. If you look at the photo imagine that the stirrup is on the ball of your foot - your posture wouldn't be too bad at all! The stirrup does already look too short though even just a couple holes (it also might not appear that way until you focus on your knee which is quite bent almost like you're sitting in a chair. That'll be those long legs working their deceptive tricks to the eye!
). And once your leg is back it would create even more of a bend in your knee which can be eliminated by lowering them a touch.
I am working with a girl at the moment that is exactly the same as you. She is always losing her stirrups and especially in the canter goes hunched over. We have been doing a lot of work in the round yard to build her confidence because this posture stems from fear. When a human feels threatened we naturally curl up into a ball to protect ourselves. You are obviously uncomfortable with stirrups which (correct me if I'm wrong) probably makes you more nervous than you would normally be without them.
I would suggest getting your instructor to keep you on the lunge like he has been doing and try this:
Let the instructor have control of the horse's head. You let go of the reins completely. 95% of riders I see these days hang off their horses heads and mouths and use the reins for balance. In the picture you don't look like you're relying on her head at all but this exercise may still be beneficial for other reasons. You can still control your horses speed with your seat and legs and if she starts going too fast than your instructor has the control of her head to slow her down.
Now sit up nice and tall. You will find you feel much more unbalanced at first because your hands have nothing to do. But this exercise frees up your brain to focus on your legs and seat. If you need more balance hold your arms out. Remember to keep your back nice and straight (but still supple).
Start at the walk (also try halting your horse without use of the reins - interesting exercise
), then the trot and once you feel the need to roll forward has been diminished you can progress to the canter.
This exercise I find really helps to switch a rider's brain from reliance on the reins to reliance on your leg and seat which are equally as important. And after time you will find that your legs feel more natural.