Hi rmerc
Well I did take a look....
I didn't find any hidden h1 tags. I took the liberty of rendering the page both with Google and my own suite of software.
You're mistaken in your analysis as far as the use of hidden h tags. Oh and yes, hidden tags are still a way to get your site demoted.
I also took a look at the backlink profile....
Again it seems you're quite mistaken in your analysis...