Maximizing life-span when running MCU from a single battery using DC-DC converter?
Nothing is wrong with your approach except for being somewhat vague.

For example i understand the intent behind "using the button that will latch the DC-DC converter enable pin", but not how a button (I assume you mean momentary switch) can "latch" anything.

In any case, I'd recommend taking a look at TPL5111 chip, which was specifically designed for applications like this.

Update:

After looking at the DC-DC specs you've provided all I can say - it is one weird device. To begin with, it's CE pin is usually connected to output (that's how they achieve auto-start, I guess). Then, if it is connected to 0 the output is equal to input?! This is not something that will give you maximum battery life! Quite the opposite, it will drain it in no time. Do not use that pin for power control.

I'd recommend either using lithium battery with TPL5110 and MOSFET, or one of the latching circuits suggested by @Passerby in the comments. In both cases the FET switches power going into DC-DC, not CE pin. 

Regarding CE pin voltage - simply connect it to output and try powering DC-DC with 0.9-1.3V. From the datasheet I suspect the way CE works is it disables some parts of the internal control logic. However the DC-DC still begins oscillation when the voltage is above 0.8V, producing some kind of non-regulated output voltage. If this output is connected to CE then when it reaches 1.6V internal regulation is enabled and chip enters normal operation mode. Which means - you should be able to start it even from drained AA.