I'm going in chronlogical order as I do with all my lists Peter Jackson Slavin Killen Joe McAuliffe Fitzsimmons Corbett Goddard Tom Sharkey Armstrong Jeffries Given the open nature of boxing in this era the divisions were more soccer style tiers of HW then they were modern weight classes. I was thinking of leaving Corbett out but I think he did enough to be picked to beat everyone not listed here. Peter Maher is next man up.
My list would, very roughly, be: Sullivan Jeffries Fitz Jackson Corbett Goddard Sharkey Slavin Maher Mitchell
Let us prepare the ground here. You basically have three definable eras there. 1. The transitional era, where former bareknuckle fighters were transitioning to Queensbury rules, and a few had considerable success, i.e. Mace, Ryan, Elliot. Jawn L comes in like a battering ram at this point. 2. The mixed era, when the world is debating which rule set is better, and Sullivan has to compete under both for his manifest sins, i.e. Mitchell, Greenfield Burke, Killrain. 3. The post bare knuckle era, where the bare knuckle rules are buried, and a new generation of Queensbury fighters are emerging, i.e. Slavin, Jackson Corbett..
Almost my list! I'd swap Kilrain, Ruhlin or Choynski in for Mitchell, but either of these four is fine by me.
I could see a case for the Ruhlin of the Sharkey rematch being ahead of Mitchell, but it seems like Mitchell was more 'game' to win, quick, tough and had better endurance than them. That Sullivan rematch may have been as much of a track-race as it was a fight but Charlie went through hell and still appeared fresh after three hours and terrible, cold rain. I know, I know; it wasn't a gloved fight, and Mitchell's gloved resume isn't exactly spectacular, but I don't think we can just discount his toughness and endurance against the best puncher of the era, alongside his abnormal speed even for his size and apparent well roundedness. Not to mention Mitchell can hit; KO'd Cleary who outweighed him by 30 pounds, apparently KO'd Slade in a private match who surely outweighed him by like 50 pounds, and it seems like he also got the better of Kilrain in their 1884 fight given how he knocked Jake down despite dropping 16 pounds to him.