Do you have access to your local windows task sheduler settings? This shouldn't require admin permissions.
If you do, you could write a simple script that runs every day, let's say in the morning when you log in, and create a (local) copy of that excel sheet with the current date in the name. That way you always have a recent copy of the sheet and don't have to search through your recycle bin or hope for appdata copies.
Something like...
Code:
REM current date in format yyyy-mm-dd
SET TODAY=%DATE:~6,4%-%DATE:~3,2%-%DATE:~0,2%
copy "X:\path\to\sheet.xls" "C:\sheet-backup\%TODAY%sheet.xls