If anything in the kickdown linkage has been changed you may not have the right parts to make it work properly. Has the carb been changed from a two barrel to a 4, if so the 1st section of linkage is different lenght and possibly the throttle cable.
I believe the carb was swapped to a Carter I have it at the carb shop right now being re built. You have a good point though. The slider shaft doesn’t seem to make sense for it..