I recommend to retrieve the last backup to your iPhone with iTunes App on your Mac in order to save your FMGo solution file.
Have your iPad connected to your Mac, select the device iPad, click on 'Apps' in the Sidebar.
You now see a list "Apps" and if you scroll down, another list with Apps which allow to transfer data between your Mac AND your iPad.
Select FileMaker Go and you'll see all FMGo files listed right. YOLu can drag and drop from OR into that list.
Maybe my screenshot will help even if it's in german language
Thank you for your post.
A three-finger swipe up and down will hide and display the toolbar that includes the folder in the upper left corner. If this happens again, try using three fingers to swipe down and reveal the folder icon.
Since you already reinstalled FileMaker Go, follow the excellent directions from "efficientbizz" (Thank you!) to retrieve your last set of files that were backed up.