“It doesn’t seem like it would be that complicated …”
Famous last words. ??
Well, you are right, it shouldn’t have been that complicated. I looked at the default widget code, and I could see exactly where to make the change you requested. Unfortunately, there was no filter available at that spot, so I couldn’t change it using the normal plugin development methods.
As a test, I hacked one of the WordPress core files and got it working in five minutes. But of course, hacking core files is not something you are ever supposed to do on a production installation.
So … I decided to extract the relevant code from default-widgets.php and create a custom widget (I had been meaning to work through the process of creating a widget anyway). Here’s the download link; you’re welcome to try it if you want.
https://www.ambrosite.com/download/recent-posts-dated-widget.zip
Like all plugins, it needs to be uploaded to the /wp-content/plugins/ directory and activated through the Plugins menu in the admin panel. It creates a widget called Recent Posts Dated which you can use in place of the default Recent Posts widget. Let me know if this is what you wanted.