The problem is you need a second serial number. The handi rifle only has one serial number. There are some older nfa registered grandfathered in survival 22lr/shotgun combos that got into the registery that came from post ww2 airforce survival kits that are registered sbs/sbr combos but those are very hard to get very rare and very pricey.
Why not just get a 45lc/410 combo revolver its basically what your trying to do. Way cheaper and easier to get.
"Gun control: The theory that a woman found dead in an alley, raped and strangled with her panty hose, is somehow morally superior to a woman explaining to police how her attacker got that fatal bullet wound." L. Neil Smith
The problem with being stupid is you cannot simply decide to stop doing dumb things...