I was going to say this was at least halfway plausible, if you believe the Harrington rumors (I don't). However, you got greedy with Salmons. Without Gordon, they need Salmons, and he is significantly more valuable than anyone they are getting.
And you have to notice that the proposed Knicks deal does not give them cap relief next season.
Ultimately, I think the Bulls just want Harrington (and I don't blame them, he would be a good fit, despite his aversion to defense) in this scenario, and I don't think Davis is anywhere near as good.