That is a 3.4 hey? I hate that engine...I think GM should have kept the 3.8 beast all the way. I wonder if they did that to lower the "average" corporate advertised MPG but my experience is that the 3.8 burns less anyway at highway speeds.
In regard to your problem - I think you have listed the options in proper order and caught with the same problem, and cautious as you mention not to exacerbate the problem, I'd certainly try 1...hoping not to have to fall back on 2, expecting not to have to resolve on 3. Please keep us posted on how it turned out.