Most of my boats seem to turn upwind; I think this is caused by the pressure of the wind on me, since my body is aft of midships. Also, the kayaks both have a tendency to turn in an arbitrary direction when I stop paddling, due to excessive underwater lateral area forward, which makes the windcocking worse. The turns get tighter and tighter until the boat is skidding sideways in one case; that sounds like your problem. In the past I have fixed this with either a rudder or an aft skeg, this makes the boats more difficult to turn however, which is a problem for me as I often paddle in narrow waters.

IMHO the remedy is to fix the two problems separately. It is particularly important to balance the boat both in air and in water for photography, so it does what you want when you want it. The skidding should be fixed with the smallest skeg that will have the boat running straight in windless conditions when paddling stops, and windcocking should be fixed by adding side area forward above the waterline - a sort of air skeg. In my experience lowering the stern by moving the seat aft does not change either problem, although it is recommended by some.

Once the lateral area of boat is balanced above and below the waterline, then a rudder can be added, and of course if a rudder is to be used all the time it's area should be subtracted from any skeg, or made large enough to make the skeg unnecessary. However, although a rudder is handy on a lake it doesn't give a kayak the agility needed to turn in a narrow river - it makes the boat less responsive to the paddle and you're better off without it. Hope that makes sense . . .