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I'd still look at the carb first - quicker and easier, fewer gaskets, fewer tools, and if you find sludge or rust particles you've probably nailed the cause. Removing the head would be next (assuming you can't see anything through the plug hole or exhaust port) knowing what you find will be more likely to be symptoms than a cause.
http://www.smellofdeath.com/lloydy/piston_diag_guide.htm and similar (I know, not a Vespa, but similar engineering) might help when peering down dark holes?
You can always blame the ethanol - it used to be quite the thing on NACC runs to blame E5 for all forms of breakdown...
Sorry mate - does sound a lot like it nipped up (seized.) not at all familiar with the engine arrangements on scooters but can you not just drop the exhaust off and stick a flashlight down the exhaust ports?
Top end rebuilds are a doddle on 2 strokes and usually pretty cheap. I wouldn't ride it any more until I'd checked it though....