Hi Mike
Not worth the effort - better concentrating on content, link building and h1 keywords repeated in the content.
Beyond h2 - doubt it'd make any difference. Page 6 is nowhere mate - 10% might make it to page 3, beyond that, very unlikely anyone would.
Taking 'bowling ball, brunswick' a search terms in google the #1 listing on page 1 (
www.bowlingball.com) has h1 and h2 tags on it's homepage. How many h4 - h6 etc ? None, although I found 1 h3 on a product page.
More importantly, that site has a crazy amount of multimedia information plus customer reviews, social media and google +1 tags ...
IMO better building content (multimedia) and communicating with the audience now that google will show reviews, ratings from +1 clicks through social media.
My 5c (but not as an SEO marketing company)
Simon