Here's what the BATF says in one of their publications:
Section 2.5 Removal of firearms from the scope of the NFA by modification/elimination of
components.
Firearms, except machineguns and silencers, that are subject to the NFA fall within the various
definitions due to specific features. If the particular feature that causes a firearm to be regulated by the
NFA is eliminated or modified, the resulting weapon is no longer an NFA weapon.
For example, a shotgun with a barrel length of 15 inches is an NFA weapon. If the 15- inch barrel is
removed and disposed of, the remaining firearm is not subject to the NFA because it has no barrel.
Likewise, if the 15 inch barrel is modified by permanently attaching an extension such that the barrel
length is at least 18 inches and the overall length of the weapon is at least 26 inches, the modified
firearm is not subject to the NFA. NOTE: an acceptable method for permanently installing a barrel
extension is by gas or electric steel seam welding or the use of high temperature silver solder having a
flow point of 1100 degrees Fahrenheit.
A shot pistol (“any other weapon”) such as an H&R Handy Gun may be removed from the NFA by
either disposing of the smooth bore barrel or permanently installing a rifled sleeve chambered to accept
a standard pistol cartridge into the smooth bore barrel. Modified by sleeving the barrel, an H&R Handy
Gun is no longer an NFA weapon because it now has a rifled bore.
Large caliber destructive devices that are not also machineguns can be removed from the NFA by
disposing of the barrel. If the barrel of a 37mm cannon is removed and disposed of, the remaining
weapon has no barrel or bore diameter. As an alternative, the barrel of a destructive device may be
functionally destroyed. To destroy the barrel of a destructive device the following operations must be
performed:
• Cut a hole, equal to the diameter of the bore, on a 90-degree angle to the axis of the bore,
through one side of the barrel in the high pressure (chamber) area.
• Weld the barrel to the receiver of the weapon.
• Weld an obstruction into the barrel to prevent the introduction of a round of ammunition.
************************
It's under Chapter 2 'what are NFA Firearms' in the NFA Handbook
here:
http://www.atf.gov/publications/firearms/nfa-handbook/**********************
Converting to a rifled bore (relining) is one option. That makes the firearm a 'handgun' and takes it out of the NFA title.
Lengthening the existing smoothbore bbl to make the bbl at least 18" AND the OAL of the Handy Gun at least 26" would do the same.
I don't believe the H&R Handy Gun has been approved by the BATF for removal from NFA restrictions in it's factory built spec(s) because of it's collector or historical value.
That has been the case for Winchester and Marlin Trapper lever action rifles. They have been allowed to be reclassified as Type I firearms and removed from NFA registration and restrictions.
Sending the H&R bbl out to be relined to CF caliber would seem to be the easiest route. Something like 38sp would be easy on the gun and make it legal.
John Taylor does excellent work.
I think the bbl may be able to be rebored/rerifled to take 45 (Long)Colt if the muzzle dia is large enough,,but it would leave the 410 chamber undisturbed for the most part,,and that may not please the folks that currently have possession of your firearm and have the final say.
..and the ATF regs above do not mention rebore/rerifling as a way to 'fix' this problem,,only 'sleeving' the original barrel.
Even if someone doing the bbl relining job did not want to rechamber the bbl (not having the receiver in hand also to check headspace,ect),,just have the relined bbl sent back. It'll fit back onto the receiver if it's machined flush with the rear of the original 410 bbl,,that in itself will satisfy the requirement of removing it from the NFA.
Once back in your hands as a 'handgun',,take it to someone else to ream the chamber out.