Oh wow, sounds like its not completely efficient...
With your LED's 'drawing' 0.55A @12V = 6.6W. With an input of 1.01A @ 9V = 9W. Efficiency = 6.6/9 = 73% - thats actually quite good given the input-output difference and current draw.
With your output voltage the same as the input voltage, the boost may have trouble keeping the output voltage at 12V, because essentially its no longer switchin the internal MOSFET, duty cycle = 0%. Tis is probably why the efficiency with 12V and 12V out isn't great. (75%).
I would work out the best current for your LED's to run at. Looking at those modules I'm assuming they have a built in current limiting resistor, so the power voltage determines the current in the LED's, and therefore the brightness. The '12V' standard might mean the LED's are running at a fairly high current which is where their brightness specs are taken from. 9V - if its enough to even overcome the forward voltage of the LED's (to actually turn them on..) the voltage left across the current limiting resistor is tiny, and so the current is much much less.
Did you try it with an input of 4.5 - 6V? It could be that the boost chip used (like so many converters) are optimsied to run at a certain duty cycle - in terms of power conversion, this means it'll be most efficient when theres a certain input voltage to output voltage ratio. Eg. 6V in, 12V out. Generally though, the smaller the difference between input and output, the more efficient - but the boost converter itself will always need some power to do its thang.
APologies if it seems like I pushed you into getting that little boost converter and it didn't live up to expectations. They *are* handy for other projects though
I bought several step down converters (8-40V in, 2-30V out @ 4A) and after a months they all found homes in battery chargers and car USB scokets.
I say, use your bench PSU to evaluate your LED modules, their current draw, with a certain voltage, and check the brightness. You might be able to change the in-built resistor to reduce how much power this disipates. Its all a comprimise of brightness, power, efficiency (larger resistor value = more power wasted) and complexity. 6W does sound like a lot, but that depends on how many LED's you're driving, and isn't totally ridiculous for battery powered apps with rechargables.
Blueteeth.
Ps. I suspect the reason you got 'pink' instead of 'white' at a lower voltage was the fact that red LED's have a much lower forward vltage than green or blue (1.7-1.9V for red vs 2.8-3.2 for green, and up to 3.6V for blue). So with a fixed voltage, the current in the green and blue dies was so low, they barely lit when compared to the red