I was going to suggest the choke, but jerry beat me to it. Apply enough choke to get the mixture down to 10 - 11 to 1 and see how it acts. The attached photo shows how I adjusted my carburetors. You need a combination of gauges to figure out what is happening. The throttle position on the far right is a simple home made gauge with a string tied to the throttle pedal, from idle to full throttle. After driving around for a while, I quickly figured out I only use the first 1/4 of the gauge, so when shopping for metering rods ( carter W-1's ) I concentrated on the first steps off idle. Full throttle was always with in range on the A/F gauge. I also replaced the linkage running the accelerator pumps and brazed the lever holes shut. I then drilled the holes back out so I eliminated all slop. The pumps move with just the slightest throttle movement. Your problem sounds like you are past the idle circuits, why the hole drilling is not effecting it, and are in the run circuit. A vacuum gauge might show how low it's dropping when it goes lean, this comes back around to the power valve spring. If you could measure when the power valve opens, you could match it's opening to the vacuum level at the time of lean running. Not sure how to measure it, but I would bet you could cure the hesitation with a spring.
