When I had a 314, which was near 20 years ago, I also had idle issues. What I found was the throttle shaft and main body throttle shaft bore had worn so much, it was leaking vast amounts of air. This was making the idle excessively lean. I found there was a kit for this in which a new throttle plate shaft, plate screws, and bushings for the main body. You drilled out the main body to accept the new bushings.
I wouldn't think there would be enough air leaking around the shaft, at mowing speed, to cause it to lean out where the exhaust was becoming that hot. I'd start by checking the timing.
I wouldn't think there would be enough air leaking around the shaft, at mowing speed, to cause it to lean out where the exhaust was becoming that hot. I'd start by checking the timing.