Hi motorman,
Icing the coils may be great way to troubleshoot this engine. the blower housing will need to be removed to get to the coils, but usually an easy job.
This method was recommended to me years ago by a MerCruiser service rep when having spark problems on a new model of inboard/outboard engine.
I do know of coils that have semi-conductors installed, it makes the spark timing much more precise, usually found on high RPM engines. A friend does maintenance on dirt bikes for a racing team. The machines are Spanish made and vintage with very limited parts available. The coils have to be rebuilt and the rebuilder uses a clear epoxy and you can see the semi-conductor thru the epoxy, kinda neat!!!
I'm not sure if small 3,600 RPM engines use this type of coil, but cooling them down may be a good start.
I have replaced coils on a 2000 or so 17 HP Kawasaki on a Toro ZTR and a 2002 or so 19 HP Kawasaki, but I don't remember what make machine. Neither machine had hourmeters, but they were high time machines. Both of these engines would quit while into an hour or so of steady mowing in warm weather. Usually would restart after cooling down for while, but the coils on the 17 HP finally failed. The still were in spec on resistance readings per the original service manual. The new coils had much different primary and secondary resistance readings and I made note in the owners service manual notes.
Both of these machines had excessive dust accumulation under the flywheels, something that I have found often and has affected the charging systems on some.
Mad Mackie in CT