Would love if this could sit more flat (perpendicular) to my wrist rather than sticking out. Maybe just need a new strap? Or anything else I can do to fix? ...
Hence a shorter strap (at least at the 12hr side) should be helpful. Perhaps a visit to the PP service center will be helpful? The staff there should know better on this issue.
Wear your watch with the crown in direction of your shoulder and you will see if the fact to change the 2 lugs fixations will resolve your feeling ;-))
I had a similar issue with an older Patek logo Deployant similar to yours' on my 5000J. Most Calatrava models require an unlined, thinner, style strap. See if your strap is too thick.