I tried this a lot. It did not work for me. But I also only sent one email and did not follow up. A few points:

1. Getting rejected does not say anything about you. The guy they hire says a lot about the company.

2. "If the interviewer(s) in question feel like you're trying to circumvent them, you're probably making your case worse"

This is the whole point. In most cased you don't deal with an expert, but with HR. HR are idiots most of the time. HR, like real estate, has also very low entrance requirements. This does not mean that all people are idiots, but the field attracts idiots.

3. A job is a sale. You have to sell yourself. And unfortunately there is only one way to make the buyer happy: Sell him what he wants, not what he needs.