Battery power to 5v led strip and 3.3v controller
A step down or buck regulator tends to be just as or better than a comparable step up or boost regulator, in terms of efficiency.  Both refer to switching regulators. There are also buck-boost regulators that can do both, allowing it to regulate through the input voltage range of a battery supply. 

You are confusing a switching step down regulator with a linear regulator, essentially a large resistor, who's efficiency goes down sharply as input - output voltage increases as well as current increases.