How exactly does someone go about acquiring something like a shotgun for home protection in a situation like this?
There is no automatic "sunset", once a felon always a felon. HOWEVER, after all legal sentence requirements are completed (time all served, not on parole or probation, etc.) the felon can petition the courts to restore their rights. Getting back the right to vote is relatively simple. Getting back the right to own firearms, isn't as simple.
There is a section of the govt (ATF, I think) that is tasked with doing investigation and review of each case for the court to use in consideration for their ruling.
However, from what I've heard, the govt has essentially refused to fund this for several years, so very little gets done. AND, there is both Federal and state law to consider. The must be appealed to, separately, and there's no guarantee that both will agree.
I've known two people, (not connected in any way), both were prohibited persons due to a youthful "felony stupid" conviction. (non violent)
One had gotten the state to restore his rights, but the Fed never did, so he's still a prohibited person, the other told me the Fed had restored his rights, but the State, wouldn't, so he's still a prohibited person as far as the state is concerned.
It is a time consuming, legal process (and therefore also expensive) and the answer (if you actually get that far) can still be "No!".
Good Luck!