I'm already using JS redirection on a number of other pages so this was my next go-to - Thanks for the suggestion. It's about 600 documents. This is a corporate intranet setup and I'm generating the document redirection using REST out of another business system.
My main concern is the lack of the stats and activity data. Oh well, my bad for assuming it would be there.
(EDIT: It turns out the JavaScript option is not valid as it only triggers on menu click, not page load - thanks Joshua-Adams for your input)
I've logged this as a question to Kentico support. I believe it's a bug.