Well thanks for the build up, but I am not that bright.
I am no expert on Villiers but the Bing carb has a predisposition to leak fuel over time. If only for the fact that the fuel in the float bowl evaporates. That drops the needle in the bowl to consume more petrol mix, if available. Any Bing owner knows that the cone on the valve can easily pick up some crude/deposits and get lodged open. High presto, with a leaking tap you have a flooded engine crank case. Now the Villiers carb may be immune to this situation. None the less sticky oil with two stroke in it suggests a dodgy tap and flooding. The Goggo actually has a pair of crankcase drain plugs for cleaning out the internal space! Such good little cars. The process as as you say.
Italian tune up is ideally driven but a static run up of reasonable revs is a neighbour annoying substitute. Something like a Villiers will clear itself of excess oil. Debate on effective oils continues and there is no doubt the some leave the internals near spotless in regular use. The older self mix or ST30 tends to leave some gum and carbon behind. This is all irrelevant for getting the Scootacar to tune, though. Talk to some experienced Villiers users, not the loudest, but the ones that do the miles without major rebuilds every 500 miles, and it will be clear what works best for these units. A joy I have yet to experience, and possibly now will not, as I am looking to downsize the collection away from Villiers machines in favour of Sachs, Goggo and Saab.