Question: A plane consistently missing the drop zone by c. 2.5 km/1.5 miles

[Mobhack]

Yes, basically don't plot a target for aircraft withinh 10 or 15 hexes of the map edge, unless you plan to approach that from far away (an opposite map edge, not the same map edge the target spot is crammed up against).

Planes need a few hexes to allow them to enter onto the map itself and if the target is too close for the entry process then they may overfly the indended spot, leading to weird target selections.