I've spent a ton of money on SEO experts making sure all my H1 tags are perfect, my meta titles and descriptions
wtbradley33 - Panda involved a combination of quality-related factors... things like fluff or derivative content, bad site structure and navigation, extremely slow-loading pages, bad design, pages that resulted in a lack of engagement, and sites that caused visitors to return to Google and repeat their searches.
There were other factors too, content duplication issues, etc... but H1 tags and meta descriptions are perhaps the last thing I'd look at to fix Panda problems. Page title elements are extremely important onpage factors, but I've seen sites buried by overoptimized titles that were chasing keywords rather than describing concepts covered by the site.
I'm going to guess that you've got algorithmic problems, and I'll take a further stab and say probably "shallow" content (ie, content that really doesn't say much). That's been at the core of most Panda problems I've seen. Weak inbound linking goes with this. It's hard to get freely given, high quality, relevant inbound links if your content isn't really good. In some competitive areas, I'd say that the content needs to be compelling.
There's no "reconsideration" fix for algorithmic problems. The site needs simply to be better (and more popular) in Google's eyes than its competitors.
I can only guess what's being done from the way you describe it, but if what you're saying reflects where your SEO experts have put their emphasis, then they may be 10 to 12 years behind, maybe more... and they may not have done much to help you.