I don't wish to scare you but that is scarey tight.
If you have a half hour delay(entirely possible) ,you will miss your paid flight with no redress other than insurance.
Cancel the award saver you have and book an earlier one.
Better still go to Athens the night before staying in the cheapest airport hotel room you can find.
Interlining should be possible via the code-share as that agreement is now with Ba but I wouldn't fancy arguing it at bag drop though.
As I said biggest worry is if your connection is delayed.