Intermittent spark might be the problem Pete - you've reported all along that you sometimes had a good spark, and sometimes none at all. I don't think it will be easy to get a Lawnboy coil in Australia, but maybe you'll be lucky, or maybe they used the same coil as some other engine. If all else fails you may be able to adapt the coil from some other engine, but as I recall the Lawnboy one was a bit weird, and as a result the design of the matching flywheel was a bit odd as well. You said earlier that the coil in your spare engine was trash.
I suggest you give the old coil a last try with the kill wire disconnected. Earlier, it seemed you were having problems with the kill wire grounding itself. To test the coil you should remove the kill wire altogether, by disconnecting it at the breaker points. If you have weak or intermittent spark with the breaker working properly, a good condenser, and no kill wire, you most likely have a bad coil.