Edit Open Graph tags for specific pages

My site: y42k.com with the current Customizr Pro and WP installs.

I’m trying to clear up a couple of Open Graph issues:
On my home page, the og:image tag is set to <meta property="og:image" content="https://s0.wp.com/i/blank.jpg" />
I’d like to be able to set that to a specific image, or set a site default for when none of the usual fallbacks are available.

On:
https://www.y42k.com/publishing-services/
The Featured Image is set to a icon image as that’s used on the front page as the thumbnail for the Featured Page link. That means that the ugly icon image is what appears when I share the page on Facebook.

I looked at a number of plugins. Many set OG defaults for the site. That fixes the home page og:image issue, but at a cost (described below).

Of the ones that let me set OG tags for specific pages, none did what I need without screwing up other things. “Facebook Open Graph, Google+ and Twitter Card Tags” probably came closest.

I have found no plugins that let me change what I want without changing many other OG tags in inappropriate ways. For example, even when I told “Facebook Open Graph, Google+ and Twitter Card Tags” not to set anything but the og:image tag, it messed with titles and descriptions site-wide, making sharing just as bad in a different way.

So what’s a focused way to edit OG tags, particularly image tags?

Note: I can do HTML/CSS, but I’m strictly cut-paste-and-tweak with PHP at this point.