Sounds like a possible air leak, not enough to show at bigger throttle openings but enough to mess up idle, possibly split inlet rubbers, spray some solvent around carbs and rubbers while idling and see if the engine picks up or splutters, if it reacts you have an air leak.
Could also be crud in the air bleed system, carb strip and blow out job.
Have you checked compressions at all, could give some clues, I've known a burnt/sticking valve to not show under power but run crap at idle.