I had another session with trackman yesterday and it confirms my current problem quite nicely: I tend to hit a lot of hooks (both straight and pull hooks) and, more rarely, pushes. Some of these are playable and might even end up as beautiful push draws but that is the exception, sadly.
The trackman numbers (for a 7i) were showing a club path of 5-10° (with very rare 2-3°) and face angles from anything between -8 to 2°, attack angles around -3 - -4,5°. I never managed to get a negative club path (without changing the setup fundamentally (i.e. aligning my feet and shoulder to the left of the target).
I will try to put a video of my current swing up as well, but that will not be possible in the next couple of days (maybe on the weekend).
Any ideas what I could check or try to see a better relation between club path and face angle? I guess my grip is fairly strong (around 3 knuckles on the left hand) and I will try a more neutral grip but what else could I do to fix this issue?