Hi Norm,
I've been caught out so many times changing coils from one motor to the next and they don't work ,so I always like to
take a coil from a good running motor when looking for problems but you don't seem to have as many mowers as I've
had with coils not working.
The first thing I usually do is check the compression so it's at least 50 psi.You could check valve clearances.
If it's low make sure the head gasket isn't leaking.
I've had a lot of motors do what you say they need a lot of spinning to start when they have very low compression but you can
feel that when you turn the motor over.
If it's a valve problem it could come good again after using the mower under load to cut grass.
You could also look for a broken or split or leaking intake manifold and check the carby O ring ,I'd check the exhaust isn't partially blocked.
Cheers
Max.