Wiring LEDs in series and parallel
I initially thought that wiring my LEDs in parallel would be best as it requires no voltage boost but I seems like it will use more battery that way.

Not really.
Assuming you have 16 leds with a 3.2V Forward Voltage @ 20mA, in series you have:

16 * 3.2V = 51.2V
51.2V * 0.02A = 1.02 Watts

In parallel, you have

16 * 0.02A = 0.32A or 320mA
320mA * 3.2V = 1.02 Watts

Same power usage.
But now you have to factor in efficiency. A boost circuit will not be 100% efficient. You are normally looking at 80~90% efficiency with a switching boost circuit. Plus the current limiting resistor used (figure 0.8V dropped.

0.8V * 0.02A = 0.016 Watts
(1.02 Watts + 0.016 Watts) / 0.85 = 1.22 Watts

And for the parallel leds, we do the same for the resistors used (figure 0.5V dropped).

0.5V * 0.02A * 16 = 0.16 Watts
0.16W + 1.02W = 1.18 Watts

In the end, we have the higher voltage, series led string as wasting slightly more power from the battery as the lower voltage, parallel led strings.