Hi Barny,
Yes, I remember the entertainment you gave us with the Levis. Definitely a bike to hang on to. Whether you eventually find a Levis engine or slowly sort out the current Villiers doesn't really matter does it.
The commonality of Villiers parts across the range means you are far from the first to have a bitsa engine. All these parts fit together without modification. For example, the original 196cc 1E engine has a cast iron piston so heavy you could use it to brain an elephant. The 196cc Super Sport piston is absolutely identical except made of much lighter aluminium. This means you can run the lighter alloy piston in a 1E with no problems. I have examples of both pistons and I'm sure Villiers used the same casting pattern for both.
Anyway, the ignition timing point for the Super Sport is 5/16"slightly more advanced then the Mk 1E at 7/32". It's a good starting point.
I am more concerned at you saying the engine has ignition from the 50's fitted. I think you can do much better with an adjustable pre-war Villiers set up (as original). This allows you to fine tune the timing with the engine running. Please tell us EXACTLY what is now fitted. A photo would be good.
After we get the ignition sorted we can start on the carb. They are dead simple but people work hard to make them complicated. They aren't.
Cheers,