And I still want someone with the recordings to get me all the "We only have X minutes" quotes and see whether they're counting down.
Confirming Rowan Sjet's observation with the following data:
The Eleventh Hour: 20 minutes until the human residence is incinerated.
The Beast Below: No obvious countdown.
Victory of the Daleks: 10 minutes until German bombers reach London.
Time of the Angels: No obvious countdown.
Flesh and Stone: One hour until the Angels drain the ship's power.
Vampires of Venice: No obvious countdown.
Amy's Choice: About 40 minutes before crashing into the cold sun.
Hungry Earth: Silurian transports to arrive in 12 minutes.
Cold Blood: Human drill set to start burrowing again in ... 15 minutes.
Mind you, I had to skim the above episodes to go to where I recalled a plot-related countdown, so I may have made minor mistakes, but I think we can abandon this possible clue.