Marlin,
Not trying to embarrass you, but you do have a highly illegal weapon (if the barrel's under 16 inches) that can land you with a federal prison sentence, hefty legal bills, and the loss of your rights to possess ANY firearm for the rest of your life.
You may be able to hide it, or hide the parts, but my best advice would be to get rid of it. If the ATF people, or local law enforcement, find you in possession (even if the parts are disassembled), it is no legal defense under federal law that you did not cut the barrel back. The issue will simply be that you have a longarm with a barrel length that required registration and a tax stamp, and neither was done anywhere along the way. As a retired LE, I can tell you that totally unforseeable occurances (fire, earthquake, burglary, etc.) frequently bring "hidden" things to the attention of the police in ways you'd never even think about.
The ATF will not allow you to register it in your name, it's beyond reason to think the laws governing that class of firearm will loosen, and you may have a hard time finding a qualified gunsmith who'd work on it to modify the barrel.
I'm all for keeping treasured family heirloom guns in the family, but you have to balance out the equation, and in this case it would not balance for me. The risk is not worth it.
Denis