Just to clarify: cranking and turning over are the same thing - when the starter motor cranks or turns the crankshaft, at the top of each stroke (both compression and exhaust, the ignition fires the spark plug.
Since you determined the kill circuit is not the issue, go back to the basics - first check the compression - as the valves and valve seats wear, the valves lose clearance and the cranking compression drops - the faster the crankshaft turns the higher the compression gets - the first clue to needing to adjust the valves is hard starting. Usually after the initial hard start, a warm engine starts easily until the next day and the situation gets progressively worse.
Not wanting to idle could be a carb or spark problem and either could be the cause of the problem. I can usually determine if it's spark or fuel by using a timing light - I connect the light and just watch the flash - if it flashing while or as it dies, then it's not normally a spark issue, but since you had the flywheel off, there is the possibility that the key sheared and the flywheel is moving while the engine is running causing the spark to be too far advanced or retarded for the engine to run.
Check the spark situation using a new other than Champion spark plug and let me know what the results are.