Welcome to using WebMention, Jeremy. Still figuring out how to best use it myself with regard to how they get displayed on my site.
Like you I use WordPress, and I would love for mentions to display more like the old pingbacks, where you’d get a snippet from the mentioning site from around where it links to you. Now it mostly is ‘site x mentioned this.’ which makes me click to get a notion if it’s relevant.
On Webmention tweaks I documented some of the things I tried. The issue is that because the tweaks are in the Semantic Linkbacks plugin, not in the WP theme, you can only make those tweaks a permanent option if it gets rolled into the plugin (no such things as a child-plugin like with themes). And I’m not confident enough of my changes to figure out and try submitting them to the maintainers of the plugin.
Replied to Now supporting Webmention by Jeremy Felt

I think? If you know how to send a Webmention, please do so that I know it works!….I’ll need to do some spelunking to figure out how I want to display and style them