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http://imageplay.net/)
Apparently the limit is 499. I think this limitation was added recently, due to potential infinite cards via reverse time + mindgate. Also, now the attack of a twinned-diving creature drops back to the original after two turns, so basically you have to use TU every single turn to keep it up. I was only able to do this in trainer.
I actually had the attack of the middle-right wyrm at 982, but it dropped to 499 when I cast TU on it. I wasn't able to see if it would have dropped anyway during its attack (like how a scarab's health changes), or if I could've broken 1000 attack by diving the 499 for a 998 and then tossing another blessing, because I had to either kill Incarnate that turn or play a sundial and then deck out.
So 499 does seem to be the stable limit, I'm guessing because 499 is also the limit for health (or maybe 500), and anything higher is unimportant because either the attack is blocked, or the opponent is dead.