The fall off between the NL Central and NL East isn't as pronounced as you claim it is. Dunn does have old player skills, so it wouldn't be surprising to see his production fall off faster as he ages, but he has 80+ power, and an extremely good eye. I don't see this collapse of production happening if he moves to the AL.
BTW, Dunn played in the NL Central for the majority of his career, and handled himself very well.