The sharer.php call definitely is an option. It was deprecated a while back, but that was removed, as the article you mention pointed out. At the time, we added the following function call to our Javascript:
jfbc.social.feedPost(title, caption, description, url, picture);
That's still available and can be used for Facebook Share features and a custom image, like:
<a onclick="jfbc.social.feedPost('My Page', 'View my great page', 'Even longer description about my great page', 'http://linktopage.com', 'http://linktoimage.jpg');><img src="shareme.png" /></a>
We plan to try to implement similar solutions for all of the sharing buttons, but right now, we don't have that ability. Some of the networks also don't have the ability to call custom code/images for sharing and will only let you use the built-in Javascript buttons.
So, going back to the original post, it's difficult to do what's imaged in the picture because not all networks we support have the ability to do that. Additionally, you mentioned you'd want custom Like and Share buttons. The code you provide above is only for Sharing. The Like button is nice to have as well since it can be a one-click option for sharing, whereas the Share button has the popup and (I don't think, though could be wrong) the sharer.php option will not increase the Like count for the page.
Lots of caveats, but as always, use what's best for your site!
I hope that helps explain further,
Alex