Pete can go in once he finishes his lifetime suspension that he agreed to.
Wouldn't work for Pete because Pete Rose has always thought that rules don't apply to him including to ones that he once agreed to.
Shoeless Joe Jackson is unique among those who are in the HOF dungeon. He was acquitted in a court of law for the offenses that have kept him from being inducted. Why not use him as a precedent? Put him in the HOF where he belongs and then state the new policy: if a player is denied admission to the HOF for serious rules transgressions, after his death, he can be reconsidered by the veterans' committee. My sympathies for these guys are all across the spectrum: high for Joe Jackson because I feel he was treated unjustly to none for Pete Rose with some of the PED users getting a smidgen of my sympathy.
The rules are there for a reason and violating major ones should have serious consequences.