H1 heading and style sheets
While an H1 heading has long been a "flag" for the search engines regarding content prioritization, the reality is using an H1 tag does not necessarily mean the text between has to be the biggest and boldest on the page.
Using either inline or external style sheets allows you to modify your H1, h2, h3 tags for font-related specs, like color, size, etc. and doesn't change the tag itself.
I do this often and have not seen any negative affects on page optimization.
Peace and prosperity.