318 Engine stumble

Those points look very worn and may be working but IMHO are essentially shot. The curvature on the points contacts is all gone. I'd get some N.O.S. ones and start over. And then set the gap for the dwell to be in the low 30's. Wear on the nubs and in the shaft bushings can be contributing to all of this. With the wear on the points, it may be time to start thinking about a different/new distributor. IMHO, there are a few areas that need work.

OK on the accelerator pump; thoughts. But if you raise the RPM's really slowly the accelerator pump plays little or no role. And if by 'feathering', you mean that you give the throttle a series of small pumps, then that means the accelerator pump is being worked to cover the flat spot. I have not gone through all the past posts.... have you checked the float level? A low float would cause problems like, or similar to, this. Same thing for the secondary stop screw adjustment being off. (Which you have been adjusting.)