The only function of the cable on a 350 is for kickdown. Just as the throttle reaches wide open, the cable should reach its full travel. Shift points on a 350 are controlled by the modulator and the governor pressure, which is generated by the speed of the driveshaft. Adjust the kickdown cable to be full forward at wide open throttle and it should function. If it doesn't, there is an internal problem with the kickdown band and/or the servo that applies it. That's overhaul territory!
Jerry

"It is better to be silent and be thought a fool than to speak and eliminate all doubt!" - Abraham Lincoln
Cringe and wail in fear, Eloi- - - - -we Morlocks are on the hunt!
There is nothing noble in being superior to your fellow man; true nobility is being superior to your former self. - Ernest Hemingway
Love your enemies and drive 'em nuts!