Small Engines (Lawn Mowers, etc.): Toro model 57360 shifting problems, clutch pedal, traction drive

Question
Stopping and shifting problem with 1980 Toro model 57360 rider mower, serial number 900972 with Tecumseh Peerless 801F 5 speed plus reverse gear transmission, serial number 4102 9793.
Can shift gears when engine not running.
Can shift gears when first started, but after cutting for a while, and trying to stop, the mower keeps pulling and am unable to shift to neutral or any other gear, unless I turn off ignition key and then shift into neutral.
I have both the operator's manual and the parts catalog for the mower,
but neither gives enough info to aid me in understanding and solving my problem.
I also changed both the blade drive belt and the traction (drive) belt with genuine
Toro belts.
There is a set of four (4) holes that allow adjustment of the deck tension arm that is connected to the idler arm and pulley. From the rear of the mower, looking from right to left, the first hole allows 2" of movement, the next one allows 1 3/4' of movement and the third hole allows 3/4' of movement. The arm was in the hole that allowed 3/4" of movement when I received the machine.

I get no vertical movement whatsoever, when the clutch actuator arm is pressing on the clutch cap, which occurs when the clutch pedal is depressed. And, both the transmission and traction belt are still turning, even though the clutch actuator bar is causing downward pressure on the clutch cap.

Can find no detailed info, concerning this mower, which is surprising since the design was basically the same from 1979 to 1986-7.  

Answer
Here's the scoop Ken.

This is a 1979 model year mower.  You have a problem called "tolerance stacking".  That's the technical term for  EVERYTHING is worn out.  

Every rod, every bushing, every pivot point, even the actuator rod, is a little worn out.  You have .020 slop here, and .050 slop here and by the time you make it to the clutch you have 3/4" of slop. That's "tolerance stacking"

Look for the sloppiest pivot area and start there.  

Thanks for the paragraph on mower deck linkage.  Don't really know what that has to do with the transmission not shifting.  It sounds like you  are suffering from a severe case of "Rocket Scientist Syndrome"  That means YOU ARE THINKING WAY TO HARD!!