Great posts. I have exactly the same LED strip, with presumably the same controller, as it came out in a kit. What I have noticed is that at White with full brightness, one portion (the end of the strip) gives out a hint of pink, instead of full white, while the beginning of the strip (near the plug) it gives out proper white. I guess it is because the drop in voltage. I'll try to solve this by feeding both ends with power. 

As far as amperage is concerned, it is obvious that the controller is limiting the amount of current so as to make white appear approximately as bright (no more, no less) than other colors, because if it went for full 6A on the white, it would appear 3 (or near three) times brighter than say pure red, pure blue, and that would presumably be a strain on the eyes. This considering that no other colour, i.e. diode combination can reach anywhere near 6 A. The controller is obviously equalizing the current so that no color appears much brighter than the next. Also, from the point of view of consumption, I am actually glad that your readings confirm what I've inferred that in no way does the strip consume full 72 watts of power at max, I find that conforting in the expectation of my next power bill. :)

But I guess increasing the voltage to 14 gives an overall brigher output, which is something I may try on my power supply. Thanks for the info.