So sounds as if tranny OK. Your original post seemed to indicate that it was not in gear, then slammed into gear when you stepped on the gas. Kickdown cable controls transmission shifting points and will not affect power output from engine. Timing will not be out unless someone moved it. Timing will not change on its own. Did you touch distributor the timing when you changed distributor cap?

"it hesitates and then races forward" Your description is not enough to go on. After the intial hesitation does car perform normally in every way? Idle normal? Was problem present only after you performed those repairs?.