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Your H1 should stand out as a solo tag and not be put into a line of code only used for SEO purposes.

Remember that H1 tags are used by Screen Readers and other such technology, read more here about the effects of screen readers and H1 tags here:
http://www.maxability.co.in/2013/06/html-5-headings-behavior-with-screen-readers/

As Google has suggested in the past, if you are doing it just for SEO and not for the user then its probably not a good idea.

My site got a revoke in May 2013 and took until the refresh in Oct 2014 for it to show recovery in SERPS

One way around this is to use hreflang and set your main site to x-default and create a new site that targets your main language.

Basically set your new domain to hreflang "EN" and you should see an instant recovery!

@ruth

I urge you to try the hreflang solution sometime as a test.

"but it's not something I would test unless you actually do have different English-speaking audiences."

You can Always set the old domain to "x-default" and the new one to "EN" so that all English search results switch to the new site, this is great for sites not willing to wait up to a year for a Penguin refresh or affected by other SERPS suppression. Both sites can be identical and will not cause duplication issues. hreflang is amazing tool for testing.

Yes that's fine, Pagerank/juice will still flow and Google will act as normal on all those child pages.

In an ideal situation you want to have good content on the pages that link to the weaker ones

Home->Landing Page->Weaker page->Child Page

Try to naturally include the most important words on the Landing Page as it will have the most power and you will be able to direct your customers through to the weaker pages.

Yes the domain does not matter.

You can even test it out with just one single page. I spoke to John Mueller about this a while ago, he said when using hreflang you can use it in the same way you use a canonical tag. So maybe you could test it on an internal page that you know should be ranking better than it currently does.

Setup the new domain, create a blank index.php page and just replicate the internal page and URL structure.

FYI, John actually talked about URL structure for hreflang just 2 days ago.
https://www.youtube.com/watch?feature=player_embedded&v=1sewHcbKTJw#t=2171

In an ideal world you want to create a clever bit of PHP so that your code is being pulled from one directory otherwise you will have 2 versions of your site that you will need to maintain and that would just be a royal pain in the a$$.

Before you do anything I suggest you read the page below and watch the video by Maile Ohye on there too.
https://support.google.com/webmasters/answer/189077?hl=en

Fell free to ask me any questions I have had to do this on a few sites and have been doing it for a long time now.

Setup your current site as the x-default and the new one as "EN" so that all english inquiries are served up by Google to your new site.

I look forward to hearing how it goes. FYI its possible you may see your results drop for a day or two and then popup with the old URL again and then the new one, It can take a few days for it to recalibrate. It can also happen right away and then random adjustments happen over the next few weeks.

Also make sure to use fetch as Google in WMT on both site pages to get Googlebot looking at your pages ASAP. I have seen results in 30 seconds before.

Question is do your customers pay to be listed with you? If so are they using you for the dofollow links? If this is the case then you may lose some of your business by changing it to nofollow.

If they are paying there is also a risk of a Google penalty for paid do follow links.

If you are unable to maintain quality and there is no good reason to have a dofollow, then switch to nofollow.

Are the pages hardcoded? Or is all the data in a database? If it is in a database it would take no time at all to run each domain through a loop and check what response status code you get.http://en.wikipedia.org/wiki/List_of_HTTP_status_codes
This would be a very quick way to find broken links. You may even be able to purchase an api on something like majestic or Moz and run the sites through that as well for a better indication of site quality. If the site has very low DA or Trust Flow, you could also make it nofollow or remove etc...

If it is all hardcoded then that would be very hard work all around.