My first thought is that the high speed circuit is not completely clean, but I prefer to do some fault isolation before tearing into the carb again.
With the engine at idle, disable each spark plug in turn. Each should cause the idle speed to drop, by a similar amount. If that doesn't happen you may have a weak or bad cylinder. A compression check would be in order.
Keep in mind that many sick engines will "run like a champ" with no load on them, sometimes on one cylinder.
If the compression checks out on a weak or dead cylinder, check the spark for a hot, blue spark that can jump at least 5/16".
Less likely but possible causes are a bent or broken reed or a leaky gasket preventing scavenging pressure in the crankcase. Gaskets tend to dry out in long storage.
If none of the above turn up a culprit I would go into the carb again, with particular attention to the orifices into the carb throat.
Good luck, and let us know what you find.
