The worst Wolverine's native/original Universe is ruled by Dr Doom
Here's a completely wild and out of the blue theory. What if the dystopian reality from which the "worst" Wolverine hails from is ruled by none other than RDJs Doom?
There would be nothing contradicting in this regard. With the X-Men dead, and Wolverine losing his mind, this world is virtually left unprotected which allows Doom to take over. I think this would be much better than introducing a brand new Universe in which Doom rules Latveria and start his narrative from there. Marvel have clearly left out some key expository info regarding that Wolverine's native world, which would allow this aspect ro be compatible with it.
Apart from this, I think there would be a deeper, superficial meaning behind this scenario. This alternate Universe is supposed to be a failed MCU/Fox verse in which things did not go well for the heroes. This "worst" Wolverine variant is clearly supposed to represent a failed incarnation of Fox verse's Logan, a celebrated hero. If, and that's a big if, if Marvel go the route of making Doom some sort of Stark variant, then this can play out very well. Like the worst Wolverine, this Universe's Dr Doom is supposed to represent a failed/twisted incarnation of MCUs Tony Stark, quite literally that Universe's saviour. Like in Earth-10005 and the Sacred Timeline, in which Logan and Stark are celebrated superheroes, in this reality, the Wolverine and Dr Doom are either failed or distorted version of themselves.
A very, very intriguing scenario.