I have just returned from the International Symposium on Domain Theory, which took place in Shijiazhuang, Hebei, China. That was a fine conference indeed. There, I met Xiaoyong Xi and Jimmie Lawson, who just happened to publish a remarkable result, related to a very recent post on coherence of dcpos: every complete lattice, and more generally every bounded-complete dcpo is well-filtered in its Scott topology. Read the full post.
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With this post, the counterexample in your last post is now easier to understand. The natural numbers with the cofinite topology is not well-filtered, so any bounded complete dcpo, which is well-filtered in the Scott topology, cannot be a dcpo model of it.