When you have backed off the piston as you have done, this is then when the points should be cracking open. Personally I never take no notice of the timing marks , as over the years mixed parts may have been fitted.
The fan on the flywheel “should” be a seperate part , and once removed you can adjust points with flywheel in place.
Some close-up pictures of your flywheel would help.

Andy.

Takes me back to the late 50s when I bought a Lambretta for a fiver that the owner had given up on. It would start and idle but not accelerate. To cut a story short the owner had managed to get it firing at around Bottom Dead Centre. That was possible as the centrifugally controlled cam inside the flywheel had been assembled 180 degrees out. Fast forward to 2009 I visited a customer to fix her ride on mower and there was a rather sorry looking Lambretta that her late husband had used for commuting around farm. A deal was done . Seemed like a good idea to convert it from points to electronic ignition . Kit fitted, pig to start and disappear in reverse – the engine was running backwards. A word with the suppliers of the ignition kit and soon sorted – I was not the first.
All of this is a long winded way of saying what others have said in far fewer words that incorrect two-stroke ignition timing can have strange effects.
A few things that can accumulate to contribute to an issue.
Points gap. Start by setting that accurately mid way between the top and bottom figure .
When positioning the piston only rotate the crank in the running direction of rotation so that any big end wear is absorbed. If you go too far don’t turn it back which will “ stretch” any slack – go right round and compress the wear again.
Then, if you can devise a way of locking the crank it will avoid the possibility of upsetting all your careful measuring while you set the point at which the contacts open.
The traditional way is with a fag paper . Correctly set up one of the windows in the flywheel will just give you room to insert it between the shut contacts and slowly turn the flywheel until you feel it start to release. At that point it’s time to tighten the flywheel nut. Villiers used to supply a couple of designs of wrenches designed to be hit with a lump hammer to ensure that the nut is good and tight. I have to say that I don’t get on with the lump hammer and wrench, I prefer a homemade flywheel band holder – a steel strap with a long handle used in conjunction with a socket on a long breaker bar. Why couldn’t Villiers give a torque setting ?
Going back to the fag paper test for determining the contact opening point , it is a bit of a three handed fiddle. Back in the 60s there was a company called Rupert Ledger who made various bits of small engine test equipment, one being the Dy-Tone – one lead connected to the HT lead and the other to any good earth. It emits an audible tone which changes the minute the contacts open. As a bonus, a fuzzy change of tone says dirty points. The other bonus is that it’s hands free so while moving the flywheel on the crank and pinching up the nut with no messing about with fag papers one’s ears look after detecting the contact opening point.