Can? Yes. About anything can be done with enough money... First seeming problem, .444 uses a .429 slug, about .43 actually, and the .410 uses a slug .41 or so or lesssss so "rebore?" Seems the hole is a bit large to start. At the same time the soft lead .410 slug with or without a sabot/cup should swage up to fill the hole and maybe even turn a bit in the rifling...
Since the .410 is very low pressure, I can guess --talk to a very good machinist-- about "bushing" the chamber area to shove the .410 projectile into the rifling... Costs money. I also think that both Marlin and Savage have made .410 shotguns on rifles standard for the .30/30... Not real common but suited to your needs.
I suspect you would be much happier with a rebarrel. In the "handi" and other single shot rifles there is a process of boring out a barrel to get a collar and fitting the new barrel into the collar. Then you don't have the "slop" and whatever "insides" you specify for the barrel, rifled, etc.
Over the years the opinion oft expressed, the .410 slug is a bit lame. Light and not going too fast. No I don't want to stand in front of one. At the same time, I don't like to see deer or other animals suffer. If you dig you can get "liners" that will slip into a 20 or 12 guage and hold and fire a .410 shell. Some were little more than a chamber insert. Some were short barrels. Some were rifled. In a break action... Another thought. But what you propose, while doable... expensive. Your bucks. Enjoy.
