Is there any way to force Google Drive products besides the drive.google.com web interface to realize new files exist?

Sharing the files to user accounts with Viewer access is one way.

From what I know, what you're getting is expected behavior. By default, files set to Anyone with the link that haven't been opened aren't fully accessible in the APIs, which is why nothing shows up in the Method: files.list of the user accounts.

I found Behaviour of "drive.file" scope on a shared folder on Google's Issue Tracker, which has a similar issue as yours. However, its current status is Won't fix (Obsolete), as this is intended.

Another one is Drive files.list returns inconsistent results when searching for files that were shared with an account via a group's member. Although this is currently Assigned, similar to the other ticket, it's likely the user hasn't opened the file shared to them, resulting in no results from the API. Feel free to +1 it if sharing with viewer permissions won't work for you or submit a feature request as this was set as a Bug.