Stiff pedal with kickdown hooked up. Help please!

If all the cable are free and move easily, and everything is fine without the TP connected then it HAS to be the TP lever or rod, or TP pressure valve spring, or a hung up TP valve.
In other words, it has to be in the valve body area.
You said you want to fix it right, so git er done and track it down.
Move the trans lever with the cable disconnected. (you did that)
Pull the pan and make sure the valve is moving in the valve body (I'd bet this is it, or the lever is not seated on the TP valve correctly)
Chk out the spring like Tracy suggests.