Only problem, if they succeed in hacking, they can do whatever they want.
GOG, could make their life and security easier (which comes with a trade off).
GOG could check against time.
To elaborate on this:
Account ABC with email XYZ registered for 1 year.
Normal user would not change email ever, or if so, they can create a delta out of it. (changed once, so delta 6 month).
If the hacking attempt is prior too this delta, ignore any e-mail change (unless done with support ticket aka like asking for a ID-card or similar) and just send an email to the user notifying him.
The same algorithm could be used for password change. If user ABC changes password every 6 month and it is being tried to change prior this delta, ignore (same would go with CC or other information). And again email to be send.
This way me thinks everything shall be fine, or? And implementing this shall be not to hard.