Hi,
Did you notice if the 7805's were hot even with the heatsink?
You didn't happen to measure the input and output voltages AT the LM7805 leads?
If peaking 1.2A, then 1.2 * 7 = 8.4Watts.
Grounds are important and I would make sure that the strip supply was star joined at the power supply.
You are using 330R that they recommend in series with the signal wire to the first 2812 of each leg?
I can imagine you would be neat with your wiring due to audio floating around as well. 
Tom... 
