ok - to complete the story of "what I should have done":
On a metal lathe, cut down a straight shank air hammer chisel to be just a hair less than 7/16 for the pilot with 9/16 for the business end of the driver.
The common air hammer I see advertised has a .401" round shank
https://www.mcmaster.com/air-hammer-chisels/but it looks like shaft on the chisel is only about 1/2" and would be too small
from the previous link you supplied for an example of an air hammer guide driver, they recommend a heavy duty air hammer
"We recommend you use a fairly powerful air hammer to drive this tool, some of the cheaper or lighter weight air hammers have problem with stuck guides."
Do you have a recommendation for an air hammer that will do the job ?
Where do you get your air hammer chisels ?