20 hp Kohler runs rough

SOURCE: I have 16 hp Craftsman riding mower with a Kohler engine.

It may think you are in reverse and is killing the motor to keep you from backing up with the blade running. Look for switch that is telling it when you are in reverse, maybe it is stuck with grass or other debris. another possibility is that the blades are jammed and they are stalliing the motor. Mines stalls easily when cold.

SOURCE: engine stalls when clutch/brake pedal is released

Under the seat, there is a operator presence switch, if this switch fails, the mower will shut off when the brake is released, or put in any gear.

SOURCE: lawn tractor won't stay running if clutch is released.

There is an operator presence switch under the seat...it is more than likely faulty and must be replaced in order for the mower to run right.

SOURCE: Craftmen tractor w/ Kohler engine stalls out continually

Sounds too lean.
Can you cover the air intake with your hand 90% or use the choke a bit and then load the engine to see if it runs better?
If you ever find a carb with manual high and low mixture adjustments that will fit yours......put it on and keep it on.
You can usually get then from older tractors.

SOURCE: Popping out exhaust, loss of power, wont run at full throttle.

I had the same problem. If it is a 2 cylinder, remove the valve covers. On one side, the rocker arm had slipped off of the push rod. It was real loose. Put the rocker arm back on the push rod and tighten it down. I think this will do the trick.