What are effective strategies for playing control against aggro-control?
You could try playing more spot removal (such as Condemn or Path to Exile) instead of mass removal. Typically aggro-control decks have problems if you succesfully remove their first threats. This way the control deck won't die in the early turns and will be in a good position to win the game, because it has a better late game.

The reason behind spot removal being better than mass removal in this kind of match-up is that it demands more answers: they only need a single counterspell to deal with your Day of Judgment, but they will need two if you play two Condemn. However, they'll need two answers if you play a second Day of Judgment, but usually you wont survive to your next turn if they counter the first one.