This may seem a bit cold, but...there is no transfer tax for a Class III (NFA) weapon from the owner to a lawful heir. This will require a form 5 be submitted to the BATF and approval given. Of course this cannot occur until the death of the owner.
Speak to a Class III dealer about the options. He may be willing to buy it from your father as it is a marketable item, or he may be able to help in the decision making process.
If it were me, I would want the gun legally in my possession after the eventual time comes. If he needs the money, you might be able to give him what the market value is and have it specifically written into the will to go to you upon his demise.
Sorry if this sounded crass or anything, dealing with a seriously ill parent is a trying ordeal.