I believe the manual cowl flaps from the J are the same (looks similar in the video), but for clarity, my experience is a J not a K.
Your description of how things used to be does not sound good. While there is some friction, pulling and pushing may take some strength to get "over-center" it should notrequire jockeying around. There 2 distinct positions, wide open and fully closed. The "trailing" position is a bit vague and is just putting the linkage over center from wide open and letting aero forces push the mechanism into some half-open condition.
There is an adjustment (very important one, in my opinion) to set how open the flaps are when the mechanism is in the closed position. Closed does not have to be truly closed. It is the threads and locknuts on the joint in your hand in the video. Some people adjust it seasonally, I just left it the same all the time. When "closed" on the panel control knob, the flaps were NOT flush, but half-inch or so, open. This helps cooling, especially in warmer weather, and gives you a very low drag setting and you do not risk overheating if you forget to open the flaps. I found this was great in cruise.
I was usually wide open on taxi and takeoff and "trail" as the control in a half-way position for climb. In some cases trail was required in cruise, such as very hot days.
If you were having trouble closing, and the flaps were set to be flush, you could also have been fighting the contact forces and deflecting the flap against the cowling.