I am not sure how it works if you delete and app you paid for. I would suspect, it you delete it, and part of the goal is to then flush all of the data, you would also flush the code that tells the app it has been paid for and thus, pay again. BUT, you also have a receipt from gMail and purchase that you bought it, so that might get them to help you out. have you tried their support options?
/** SGS3 (rooted & stock ROM) **/
/** Asus Prime TF201 (rooted & mildly OC'd) BRICKED BY THE ASUS OTA JB UPATE!**/
/** OG Droid (rooted & OC'd & all hacked up) **/