He has swapped in another carburetor which made no difference whatsoever.
The bucking which is going on does not seem to significantly alter the RPM of the engine to my ear, nor the power of the engine judging from the seat of my pants.
This 216 has 30,000 original miles on it and is very strong. It likely has been sitting for some time though. He bought it used from a little old lady recently and hasn't driven it much at all.
For now, I am going to recommend that he drive it to see if it gets worse before it gets better.
I'll let him know to do the fuel pump volume test just in case my ear and the seat of my pants is out of calibration.