Do you have another power supply you could try? What exactly do you mean by poor sound? Are there any fans or anything running off the 12V? The audio curcuits use the +12V and -12V supply rails.
What revision is your A1200? There's a video on YouTube I recall whereby the chap was investigating distorted audio on a 1A revision board and the problem was that the audio was too loud which was distorting the inputs to the amplifier/tv audio in etc. He discovered that the board had incorrect smd resistors fitted in the opamp circuit which he duly corrected. How does the volume of your A1200 compare with your A500?
Other than that, yes caps are a good start and the audio caps are known to have caused distorted audio on those machines where audio caps are leaking.
