Gregory, I am not familiar with Kirkland's Guns. Is this one of the old Turner Kirkland Belgian-made single shots? Maybe a custom builder? Can you provide a photo or two?
You described breaking the ramrod you were using before. I see "the ramrod slot" measures .288", but I don't see the bore size mentioned. If you are shooting a tight-fitting ball and patch combination, there will be a great deal of stress placed on a very small-diameter wooden ramrod. If it were mine, I might make a replacement wooden rod to put in the ramrod channel of the pistol "for show," but I would seriously think about a brass or aluminum rod for actual loading and cleaning. A quarter-inch rod would probably do the trick, but again, we don't know the bore size which would more likely dictate the diameter of your loading rod. You might be able to go a little larger.
Anyway, one way to "turn down" your wooden rod would be to chuck it in a hand-held electric drill. Wrap the rod loosely with sandpaper held in your other hand. Work the rod back and forth in the sandpaper while the rod is rotating at low speed, and you would be surprised at how easy it is to reduce the diameter. If you start with a slightly larger diameter rod, you can turn a nice taper in it, as the old ones were done.
Good shooting, and be safe! ... and please show us some photos of the pistol, if you can manage it.
Notchy Bob