Hi Arnoud - I post over on Dr. Squat's forum too, saw your question here.
Is there any way to take a video of you doing the deads, or even a pic of the starting position? It's a LOT easier to figure out using visuals, but some ideas that are usually culprits:
1) Calf flexibility, specifically soleus. You have to dorsiflex considerably at the ankle to get down low enough to get into proper position, MUCH more than most powerlifting movements. My knees are usually about 4 inches in front of my toes on snatch grip deads off a podium and full squats.
2) Glute inflexibility. Have you checked out the Get Your Butt in Gear series on this site? The stretches mentioned would give you a good idea of how your glute flexibility is doing; even if your hamstrings are flexible, you won't get into proper position if there's some tightness or adhesions in the glutes.
3) Tight shoulder internal rotators. If these are tight, it's going to pull your shoulders forward and thus round your back with a snatch grip in the deep position.
4) Adductor tightness. Not usually a problem, but it would effect hip flexibility in a deep squat position.
One of those is probably the problem - let me know if all these are loose/stretching doesn't help the problem.
Have a good one,