Hey folks, just did the quest today. Since everything appeared random I figured it all up on my own. Here's my breakdown of it and how to win against that annoying engine.
First, I did the math on the boxes (all measurements in millisprockets):
From large to small, their contents weigh:
4956 ms
1920 ms
3991 ms
2000 ms
3000 ms
So, if you place the largest and smallest boxes on one side, and all other boxes on the opposite side (doesn't matter which goes starboard and which goes port) you end up with 7956 millisprockets on one side and 7911 millisprockets on the other.
Moving on to the map, if you read the book second book on the table, it tells you what the stars look like. For instance: Star of Ak'Anon is a lone bright star; cog of cobbleknob is one star surrounded by 8; the malfunctioning gadget is one star surrounded by four, etc.
Point yourself north, peer. Turn 45° clockwise, repeat until you've made a full circle. Note what constellations you saw at what positions. Right click the machine, dial the constellations in order.
Now, for the hard part.
The it's easy to get the engine to the first four steps. But figured out a pair of tricks to get it started. One way, is to pick up your mouse with one hand once it's over the engine, and tense up your arm so that your finger shakes violently against the button. Old skool turbo trick I used for NES. That's how I got it started. Another way, if the keyboard is easier for ya, zoom in so that the engine is all you see, and mash the F key as fast as you can. Alternatively, do both simultaneously. After a short while you'll see a ghost emanate from the engine. KEEP GOING!
Even if you let up briefly, that doesn't mean you'll lose. I did, and still got it started, so it would appear that you have to interact a specific number of times, not a specific rate of speed. You'll get several warnings that the machine is shutting down until you get it started, don't let this discourage you. You'll know that you got it when you see the machine "Vroom".
After you do this, you'll be on an island with the captain in a cage and a bunch of pirates. They come 2-9 at a time, depending which group. They're really annoying, I soloed it as a 25 templar with 31 aa, took two attempts. If you think you're going to die, DO NOT zone out via the ladder on the boat, it takes you to qeynos harbor. If you just die, you respawn at the boat. You can go back in and try again, but you'll be starting over from scratch. Use your long cooldown abilities if you have to on the first pull of 9, but wait until they're fully refreshed before taking on One Eye. The first groups don't respawn unless you zone out, and you will need it. The entire right side of my screen had a tower of negative effects 5 seconds into the fight. Hope this helps you folks!