Hey Miller,
Thanks. I keep researching the .44 Shot. Everytime I think I have found the end of the trail, some new information pops up. Yes, the H&R singles are nice light guns.
Loren,
If the gun you are talking is a true take down model, with the quick release on the left side, then the earliest possible production date would be 1903. By the way, if you have a Harrington & Richardson double barrel in 44 Shot just laying around, let me know.
Researcher,
I have several boxes of these shells sitting here; black powder, semi-smokeless (with the gun cotton) and some kleen-bore. If you ever want to relive your youth, let me know.

Pete