At a regular REL Vintage event (yes, we have those at our FLGS), you are called over by a player's opponent after that player has announced he is casting his second copy of a restricted card. What's the fix?

It's regular, so I really don't want to hand out a game loss. But I'm not sure how to actually repair the game state. If it was legacy and a banned card, the JAR instructs me to replace the illegal card with a basic land and back up the game state to before the spell was cast. But I'm hesitant to apply that fix to a restricted card, since swapping the second copy for a basic still leaves the player with a significant advantage: they had four chances to draw the “one-of” card instead of just one.

It's regular REL. If we aren't worried about cheating, I would say to allow the 1st casting, back up the 2nd casting replace that card and all other copies with a basic land. Now the player knows and we shouldn't have to worry about it again.

I agree, just fix the deck now that we know it's not legal, and re-draw after shuffling. Make sure the player knows what's legal for the format (only one Brainstorm), and they won't do it again.