The problem is a combination of slack in the throttle cable, governor spring tension or slack at idle, and the throw radius of the throttle control on the engine. The problem is by adjustment for one thing you screw up something else.. So basically you can't do much for it. I see this problem on Husqvarna, and poulan riders all the time. there really isn't a fix that I have found.
It would effect rpm's to the deck, clogging could be related or not. Move the throttle to the full open position. loosen the bolt holding the clamp on the engine, and pull the cable to fully open the throttle, and then tighten the clamp back down.
If the clogged deck is pulling the engine down and killing it that is one thing, If he is loosing power and dying that is another.
The rough running could be due to a fuel delivery problem. Something effecting the fuel solenoid on the carb, or clogged fuel filter, fuel line, or possible fuel pump problems.
It almost sounds like he is running short of fuel. And after disengaging the pto, the fuel system catches up.