After searching online, the best solution I’ve found so far is to just make a symbolic link in either ‘/Library/logs/’ or ‘~/Library/logs/’ to get it to show up in the Console application.
I’m wondering if it would be possible to add a new directory or log file to the ‘root’ level directly under the ‘LOG FILES’ section in the console.
Here’s a quick screenshot:

I don’t believe it’s possible.
If you’re generating log files, you should generate them into one of the standard locations anyway, so this won’t be an issue.