I suppose you use a bridge rectifier between generator coil and DC-DC converter? don´t skip that.
In the end work or work not of any ECU boils down to the crank signal. If it is unstable, anything else is useless.
How do you manage it?
I have not even an idea how a Vespa engine is build, even as I was considered a local 2-stroke specialist 45 years ago
Even as the two stroke engine, in the real world, is virtually dead because of emissions, fitting an ECU to it seems quite interesting.
In (my) theory, tuning the fuel could be quite a challenge, the moment the exhaust gets in resonance.
If you want hints that really help, post pictures, even if you are not too proud of you "Test" constructions. This way someone here maybe can give you ideas what can work and where you chase a dead end.
Today we can do things to such engines, that a few years ago was impossible for DIYS and even manufacturers where not able to do, because of huge investments. Fuel pumps and ECU units have become so small, you can fit them into a lawn mower today.
The improvement on two stroke´s fuel consumption should be impressive.