I have been working on this question. Let me restate the question that I have been trying to answer.
This is the paradox, how can iodide be a good leaving group and a good nucleophile? I think the answer is polarization. A good leaving group and the high acidity of HI shows the electrons are being pulled by a larger nucleus. This also creates a greater repulsive field to a proton. Combined, this results in a greater acidity. The only reason I can think for iodide to be a good nucleophile is for its outer electrons to shift to a greater distance from the nucleus where the repulsion would be less and increase the attractive field of the electrons.
In order for this to happen, I need to show electrons can move or shift their positions. This is easy, nitrogen inversion (see Wikipedia) and resonance. We can call a shift or movement polarization. Now, we can combine two effects, polarization and size (number of shells). Pearson had described a kind of this effect in "Hard and soft acids and bases". Larger atoms are softer (more polariziable) than smaller atoms. If so, then iodide, if it's electrons can momentarily shift their positions, can react as a nucleophile.
If this same polarization effect were to apply to thioamides, then a momentary shift in its electrons can extend the reach of the electrons and result in its being a better nucleophile. (I use the same argument to explain why an enolate should react at carbon, also described as the rule of the boxer, a longer reach connects first.)