Prevenient grace and Romans 3
Prevenient grace basically defeats the purpose of Romans 3. Not by denying it: Romans 3 stays true, but it gets turned into a lower layer, a description of what we would be on our own, with a second layer sitting on top of it. The second layer is grace applied to everyone, and it is the only one anybody actually lives in. So when you say there is none righteous, no not one, you have to say which layer you mean, because on that account the sentence is never true of anyone you have met.
Where I land
I agree with part of the premise. Human nature is not something apart from God, since we are made in his image. But we have defiled that image, and in that sense we are separated from him.
Here is the split. Our mere nature just is the defiled image, and all of Romans 3 is true of us right now, in reality. There is no second state stacked on top of it. God gives grace, yes, but the grace he gives does not make us better. I mean that generally, about human beings as such, not about what he does in the man he regenerates.
What I still have to check
Whether that is actually their position, put that way, or whether I have rebuilt it into something easier to answer. Worth reading Wesleyan and Arminian writers in their own words before I set any of this down as a position.