go back to your original layout, moving the div's around will not work.
a couple of points...
1. Although having h1 before h3 is advisable, (though even facebook and myspace have h2 lead with h2 tags) many other factors affect search engine rankings, such as title and content meta tags.
2. Why don't you try changing your jquery accordion css, so that the tags are h1 but are sizes as h3. the appearence will be the same, and it overcomes your problem.