[Daves55Sedan]

Ummm, hate to tell you this, but the reason you are experiencing slipping of that linkage is because you are missing a tension spring between the upper and lower sprags of that kickdown element.
The reason they have that slot in there is so you can punch the gas pedal and achieve intermediate gear kickdown without damaging carburetor butterfly valve shaft and associated linkage. That spring takes up the slack, but during normal driving the spring holds that kickdown element steady.
I suggest NOT using your passing gear kickdown until you can replace that missing spring and pull that piece of plastic tubing out of there. Once that spring is put back, you should be good as new.