A cold plug has a smaller space between the electrode and the case so less flame gets into the space the electrode runs cooler but that means it gets more soot and doesn't get burned clean. So I would expect no difference when the plugs are new but if its been run a bit they may be sooty. You could clean them and try again but I doubt its the cause of poor starting. Having run a BSA on plugs that were too cold it started and ran fine but oiled up in traffic and misfired until I got back on the open road.
You have had work done on both the ignition and the carburetor so its very hard to know. Thinking out loud here:
Get a spare plug and kick it over like you would for starting, is there a good spark?
If its manual advance see how this affects the spark, it may be weak at full retard. Does it kick back on full advance? (it should)
When it fails to start are the plugs wet?
Can you bump start it?
This may or may not be relevant, but I have just put a Matchless together with a rebuilt and rather stiff engine. It was almost impossible to get enough speed on the kick to get a decent spark. In the end I got a roller / paddock starter and used that. That allowed me to get it running and set the idle mixture and after 10 or so starts and about 1 hour's running the engine is free and starts fine on the kick-start.
