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Firstly make sure you have no on-site references to index.html else you'll be distilling your link juice. Ensure all references to you home page are www.mysite.com/

For the redirect try the following:

RewriteCond %{THE_REQUEST} ^[A-Z]{3,9}\ /index.html\ HTTP/
RewriteRule ^index.html$ http://www.mysite.com/ [R=301,L]

Just thought I'd revisit this discussion to see if there's been any movement.  Any updates for us at all?

You can still utilise the old way of sharing on facebook from your content with a simple URL..

You could either use an image link, or text link but the main guts is the URL..

http://www.facebook.com/sharer.php?u=<url to="" share="">&t=The%20Title%20To%Share

That's it in a nutshell. Replace the 'u' parameter with the URL to share, and the 't' parameter with an escaped title. I've added %20 to show spaces in the example. </url>