I don't think app-to-user requests are going to get you what you want. As they can only be sent to current app users.
From: https://developers.facebook.com/docs/requests/
App To User Requests
App to User Requests can be used to re-engage a user in your app and
can only be sent to users that have installed the app. For example,
notifying a user that something has changed since their last visit,
"10 of your friends are now online".
App to User Request are sent via the Graph API, for more information
see the apprequests docs. App to User Requests are only available for
Canvas apps, not websites, as accepting a request will direct the user
to the Canvas Page URL of the app that sent the Request. Notifying
Users of a App Request
App to User Requests do not create notifications, though they do
appear in the App and Games Dashboard and increment an app bookmark
counter, similar to User to User Requests. Accepting an App Request
This process is identical to accepting a User to User Request.
From https://developers.facebook.com/docs/reference/api/user/#apprequests
Create
You can post a apprequest for a user by issuing an HTTP POST request
to /USER_ID/apprequests with the app access_token.
Note: POSTing to the Graph API endpoint of /USER_ID/apprequests is
considered an App to User Request. App-Generated Requests do not
receive notifications and get limited distribution in comparison to
User to User Requests sent with the Request Dialog