Everything I'm talking about below is not new, but I thought it was an interesting idea and realized I already had the majority of pieces in place to play with it. I want to share what I learned. If you are at all interested in exploring this topic further a good paper on it is here. Also, a few years ago IOActive published a blog post on the technique which is also a good read. Finally, the last two paragraphs in section 6 of RFC5246 clearly document the problem the best I've been able to find:
Any protocol designed for use over TLS must be carefully designed to deal with all possible attacks against it. As a practical matter, this means that the protocol designer must be aware of what security properties TLS does and does not provide and cannot safely rely on the latter.