Warkton Tornado No.1 wrote:The problem still sounds to me as though it is on the crankshaft axis. Even SIP & BGM can cock up

& sometimes the woodruff key can be an interference fit on height. You can chase your own tail for ages on that

I keep some that I have had to trim, step or even make from thicker material & step to remind me that we are in current day Lambretta World where quality is often only an option.
Is the front sprocket fully concentric, although clutch sprocket/clutch assemblies can run out of true?
If you are struggling, I must have a dozen or so 15 T sprockets (all Innocenti) of which I'm happy to send if it helps you eliminate it from your enquiries
Another option might be to remove the sprocket & chain & start up via the flywheel side (if you dare!) using a good drill & socket.
Not an impact driver as that will just rattle the nut off. Another option, sometimes used on race machines, is to make a simple bayonet fitting. Using a flywheel puller would suffice & be even better than using the 17 mm AF LH flywheel nut, as both inner & outer threads are RH. With the puller fully inserted & the central screw locked in place with a nut, (usually M12) it would serve the same, temporary purpose.
It's not as mad as it might seem & I often strobe up an engine with the latter method prior to starting as a good benchmark setting, but I confess to never having started an engine in that manner, simply because of the load inflicted upon the crankshaft if all off the transmission is connected. It hadn't ought to be an issue with the chain off though.