So, I'm not sure if anyone else has thought about this, but here's the thought:
Demolisher: "During your activation, you can perform 1 of your attacks after you perform a maneuver."
Engine Techs: "After you execute a maneuver, you may exhaust this card to execute a speed-1 maneuver."
With the way this is worded, with both of these abilities' activations happening at the same time (after performing a maneuver), then I understand it to be that choose to do one or the other in whichever order you find most useful at the time. It's important to note that neither one says "Immediately after", which is the usual context that Fantasy Flight games has for saying that one must happen right after the other, with nothing between.
The tactical implications are great. You can use this to either get closer to your opponent before firing, or if you're already close enough, you can do your first maneuver, fire, and then use your Engine Techs maneuver to move to a more advantageous defensive position.
What're your thoughts.