I finally got annoyed enough at Microsoft not using standard methods to record recent files in the Mac Office apps that I wrote some LaunchBar actions for them.
This requires Office 2016 or 365 (application versions 15.x). Earlier versions store their recent files in a different format so it won't work with them.
You don't have to use the actions directly; you should just be able to hit the right arrow after picking Word/Excel/PowerPoint in LaunchBar, if everything works as expected.
If they work for some other folks, I'll make more of an official release...
Here's the download.
You'll need to open each action separately as LaunchBar doesn't want to install 3 actions at once.