The current .410 shell is an outgrowth of .44 shot cartridges from the late 19th and early 20th century. It is quite possible that someone rechambered an old H&R to 3 inch .410.
You really need a chamber cast to find out what you are dealing with. Get your gunsmith to do it or order Cerrosafe from Brownell's and follow the directions. You can also do a sulphur cast, but that is a stinky job with a fire risk.
Once you have the chamber dimensions, you can figure out what you really have. I seem to recall there were several lengths of .44 shot cartridges. The only such gun I ever worked with was Hopkins & Allen. Shortened .444 Marlin brass worked in it. You may have to thin the rim to use .444 brass.