One point you should consider with the Mimik--the last I heard, Linn has discontinued service support (at least for some sorts of repairs) on its older CD players. I think this includes the Mimik--and if doesn't, it probably will in time. (Of course, servicing an older CD player may not be worth it--but I myself like to keep as many options open as possible.)
I heard the Mimik once. It's not a bad CD player, as I recall, but I didn't think it was a big enough improvement over a cheaper Rotel to justify the price. More to the point, my somewhat fuzzy memories suggest that it may not have the pace, rhythm, and timing that you're looking for.
One other possibility that MIGHT work is an older Naim player. I think I've seen these go for about what you're interested in spending. I haven't heard a Naim CD player, but given the nature of the company's products, I'd guess there's a good chance that they'd have what you're looking for. The one major hitch may be, again, service (although I've heard good things about Naim.) Then, some say that Naim CD players only work well in all-Naim systems.