I recommend that you put the carburetor back to standard condition in every way that it has been changed, Paul.
The objective with diagnostic processes is to find the cause, which is usually a single cause. That implies that everything that has been changed, should be restored to original condition immediately after the test that was made with that single item changed. If you don't do that you can develop new problems due to the changes that have been made, and it can become impossible to isolate the original problem.
It sounds as if we now have evidence that the Millers Falls engine has a good ignition system. We don't know at this point what the problem was, so we want to get the engine into its original condition, except with the electricals disconnected from the mower. If we can get it running like a new one under those conditions, we can start to examine the electrical connections in detail.