Joe, I do not have an answer for you. As Scott pointed out, the tools you mentioned could have been pressed into service, and served the gunner well.
One thing on gimlets is the shaft size needs to be under 2\10th's of an inch to fit the vent of the gun. And it has to be long enough to penetrate through the thick casting of the breech and be able to clear out an obstruction, so length matters.
The engravers tool \ Bormann fuze punch has supposedly been dug in artillery positions before - supposedly. I bought one dug at Dalton the other day, and have seen actually quite a few dug ones around. All supposedly came out of artillery emplacements- supposedly. But with that said,I wouldn't think that this tool was used around the 1800's home, can't think what for, so I think it would be rare to dig one at a home site. So maybe they were readily pressed into service. The flat edge would keep them from rolling off the limber chest lid. [ or the drafting table of an engraver ]
The Mordecai drawings do show a US issue Bormann fuze punch, which looks way different than the brass ones. It also has a gimlet in there too