The administrative rules regarding the intoxilyzer device require a twenty minute observation period. This means that the officers must observe you for at least twenty minutes prior to beginning the test. The purpose is to make sure that any mouth alcohol clears up so that the results are not skewed by alcohol actually being in your mouth, creating a higher result.
Having said that, they do not need to observe you for twenty minutes from arriving at the testing location, just twenty minutes from the time of the stop. Further, coughing is generally not considered to create a problem. In short, the issues you have raised would not make the results inadmissible in court.
The better argument is that the results are just over the limit anyway. As you may know, if you blow quite high, perhaps .15 or higher, then the prosecutor would have a good case and likely not be willing to negotiate. However, with a .08, the prosecutor does not have a compelling case and may very well be willing to reduce the charge or at least provide a reasonable resolution.
As to your questions regarding the ultimate result, it would be impossible to state with any certainty how the case will be resolved, there are just too many factors to be considered. But, considering the amount of jail time you have already served, your suggestion of house arrest appears reasonable, especially in light of the low breath test results.
Also, several customers have asked how they may direct a question to me in particular. If you specifically want me to assist you in your legal matter, just put "FOR JOSEPH" in the subject line and I will gladly pick up the question as soon as I am on-line.