OK, let's see how this goes.

Frequency = 20,000Hz
1/(2*PI*frequency*cap value) gives 36.2Ohms for the cap.
36.2 + 2.2 = 38.4Ohms total accross the resistor and capacitor.

30VA 12-0-12 supply gives 2.5A max.
I'm basing the current through the resistor on the difference between the resistor/cap and the speaker. I would say roughly 17% of the current should go through the resistor/cap.
2.5 * 0.17 = 0.425 through the resistor/cap.
0.425 * 0.425 * 2.2 = 0.4W.

0.4W is much better. If I used a 470nF as the datasheet suggests then I work it out to be 1.4W though which still seems a little high but it's still much better than before.