I had a similar problem, except it sputtered on low end all the time. I got fed up and bought new PWK 30mm, jetted at the factory for my shee. Still sputtered on bottom. I adjusted the air screw leaner and put my needle at the leanest position It had previously been at the next to leanest pos. It screamed after that.
When I still had stock carbs, I also put the stock pilot back in (going down from the #30 I had in it). It didn't work.
You'll get much better advice than this, but just my 0.02.