What we did, was slowly to integrate new HTML elements, such as section, article, and header. These elements did not effect the SEO of our pages in the wrong direction, after months in place.
The new Redesign
Brugbart was recently redesigned, and now we strictly use h1s for subsections. The new site attempts to follow the new HTML standard very closely. We don't think this change will effect the site negatively, since we have used multiple h1s for menu headings before, without seeing any drops in the SERPs.
Also keep in mind what Matt Cutts stated about using multiple H1s.
If there is a logical reason to have multiple sections, its not so bad to have multiple h1s.
He also gives an extreme example, which could have a negative effect.
I would pay attention to overdoing it, if your entire page is h1, that looks pretty Creti, right?
Multiple h1s good or bad?
Maybe it did have some effect in the past, who knows? But it sure doesn't seem to matter now. Whether Google understands the new sectioning system is irrelevant, because it doesn't need to know the individual sectioning levels to rank a site. If it sees something it doesn't recognize, it will simply ignore it, for the most part.
I'm sure many of you have seen cases where someone would pretty much replace headings with strong elements, or the other way around, and still get good rankings. There is a tolerance factor for each site, and generally a reputable site will be able to get away with more mess, than a site that was just made.