Understanding Power/Current/Voltage drawn by LED Strips
Although you give clear voltage and current readings, you are ignoring the Load Regulation error and impedance of the source being transformed inefficiently to the load.  The battery ESR is the inverse of its load-regulation error and boosting a single cell's voltage by a factor of 4 increases the impedance by 4^2=16 at 12.5V which degrades load regulation by the same.  This is why Approach 3 was best by increasing the battery capacity in VA-h = Wh by a factor of 4 (cells) and ESR x4 without the expected 10~20% converter losses.

In general, it is always best to match the battery voltage range to the load and have a source impedance much lower than the load and have enough Wh capacity to exceed your requirement as using &lt; 20h can often supply less than Ah than rating.  So compare your Watt supply to requirements conservatively and match voltage without conversions unless you understand the specs for conversion losses.