Hi Steve,

I've had lots of coils and spark plugs break down once they get warm after running for a few minutes.

The proper way to test a coil is a load tester that most people don't have ,when the coil is really bad it
will show up just with an ohm meter ,the only other way is to check for spark or check the resistance of
the coil after the motor stops.

You said you had no spark after the motor was hot and as long as there is no seat kill switch or other kill switch shorting out
( sounds like there can't be if you have run with the coil kill wire disconnected and it cuts out ) and if it's not a fuel problem
like the carby not getting fuel as some motors have a electric fuel cut out.

It may be worth using the mower close to home or just run the mower for half an hour if it cuts out with no spark ,send the coil back for a replacement.

Cheers
Max.