Following Mike Harrell's suggestions, the Oct. 2011 "Handloader" (#274) magazine has an article showing how to convert .44 Spl. to .44 Henry in the same way Mike shows for his Wesson. Of course it shows how to convert for a .44 Henry Colt SAA, and your Ballard may use a different .44 RF, but using the same method with a .44 Russian, .44 Spl.,.44 Mag or cut down .444 case oughta cover about ALL the many .44 RFs.
If your bore is really toast, you could get it relined with a .44 liner and just use these .44 CFs converted to RF. That would leave it "cosmetically historical" at least. A GOOD reline doesn't show at all on the outside.... Just some thoughts. Nothing wrong with the original concept; I too love .22 single shots.