I am going into a telephone pre-screen interview before this construction employer decides to fly me to their headquarters. I am ready to start demonstrating that I can do this job. I do not have enough information about the interviewer to determine their comfort level. Should I react 'normally' during this interview or should I try and divert conversation to how I would do the job?

First, you can only do this on the phone with the hiring manager, not with HR. Second, never "divert" a conversation -- not on the phone, and not in person. "Guide" is more like it. It takes a little finesse, and a little diplomacy. If you're unsure how to bring it up, ask the interviewer, "Would you like me to give you an idea of how I'd tackle this job?" Then take the interviewer's lead, especially if you're on the phone. If you don't know anything about the interviewer, let them take the lead in the discussion, then at a comfortable point ask what brought him or her to this construction employer, and what it is about their current project that they find challenging. This is a good way to steer the discussion toward the work. Not all managers feel comfortable with construction executive job seekers who are ready to show their stuff. You have to make them feel it's their choice to let you do this. So be gentle. If you're talking with a good manager, they'll give you some room.
Try no to present yourself as a know-it-all, or like someone who thinks s/he's going to step in and "take over". Take it slow. Show what you can do "with permission", and then ask the manager for their feedback.