Torqueflite 727-904??

Per post #5, it seems you may have the wrong Throttle cable bracket.
A 4bbl Throttle cable bracket is different from a 2bbl, and so is the linkrod from the carb to the KD pin. The 2bbl bracket will give you both of the symptoms that you describe.
Whatever you do; do NOT anchor the throttle cable by clamping it on the outside black plastic covered sheath! It has to be clamped on the shiny metal tube-part.