Setting up a download page requiring a user to fill a form before downloading anything
There is Webform Protected Downloads. But it will result to quite a different structure from yours. Webform Protected Downloads allows someone to download a "protected" file after filling out a webform. You can add more than one file and have the download links expire after a certain time.

When also looking for something like your issue I also found another module (don't remember the name) that added a page before redirecting you to a node. So maybe you could add a webform page to send the user before reaching the download page. But if he knows the link he could bypass it of course.