Lack of piston wash is an indication of lean jetting, shiny pistons with no carbon would indicate very rich.
But, you are describing symptoms of lean at low throttle settings, it's entirely possible (maybe even common) to be lean at low throttle settings and rich at wide open throttle.
When you have a situation where opening the throttle suddenly make the engine hesitate or die, but opening slowly doesn't, or at least isn't as bad, that's classic indication of low speed jetting too lean (really low throttle jetting would be a more accurate term, but people say low speed)
What happens is, if you are tooling along at just off idle or low throttle and your mixture is good enough to run but a little on the lean side, you open up the throttle quickly and suddenly there is a bunch more air, but the fuel takes longer to get there, so momentarily it's too lean to run, engine dies, or at least hesitates.
If the progression holes are plugged, you can get weird situation where one specific throttle opening it will run but then you open the throttle past the next progression hole and it won't, it will be weird, but in general, lean on the low speed.
Making sure your carbs are good and clean is easy and free. Just do it. Make sure those progression holes are clean.