Create a custom SharePoint list that contains 2 columns (the filename of the report and the doc lib path). Create a custom SharePoint webpart to iterate over that custom list, go grab the actual file and show the properties that you want, add this custom webpart to your site page somewhere.
If you want to go further, you can add a custom action that will add / remove the report to / from the custom list and attach it to all those document libraries so user can easily manage which report to show in your custom page.