I have returned, with SCIENCE!
Thanks for the good advice, Aeson and Berny! I used to assume that the “engage distance” order controlled both moving to and retreat from distance, so now I’m realizing things are very different. Does anyone know if this “Retreat at half the engagement distance” behavior was made to intentionally balance the game by preventing Missile ships from effectively staying out of range or something?
Anyway, onto my findings, (which basically just confirm everything you guys have already been saying anyway, but this way I got to make spaceships fight for science).
I issued a Challenge to myself just so I could put this issue to rest for myself
I made some test targets that were slow, with big shields, and close engagements orders, as the enemy. They were intended to slowly creep up to my missile ships. Then for my missile ships, I made very fast ships with long range (1100 meter) missiles, set to engage at 1500 meters.
Without “Keep Moving,” my missile ships would move to be exactly 1500 meters away from their target, then stop (unless they already started out close enough). As their target kept coming at them, eventually when the target was 750 meters away, my missile ships would keep doing little jerky bursts to always stay exactly 750 meters away. This finally ended up with them all stuck in what I dub the Berny Spacial Boundary Corner, because the captains were under such strict orders to never be within 750 meters from the enemy, when the enemy had them pinned in a corner they wouldn’t even move to get out of the way and get farther away, because that would involve briefly moving closer to the target for a moment in order to get around them
Very literal, these captains…
With “Keep Moving” on, they would sort of dance back and forth to the target (not orbiting it like a satellite, but more like a wonky yo-yo coming back and forth while wiggling), pretty much always being between 750 and 1500 meters away… until they got stuck in a corner XD
SO, for situations where you have a ship with longer range weapons than your enemy, from this I can conclude:
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If you want to make absolutely sure your ship always at least attempts to stay out of the enemy’s weapon range (provided you are fast enough and there is room for them to go), you need to set their engagement distance to more than double whatever the enemy’s effective weapon range is. (This is assuming that your weapon range can still reach them at half of whatever range you set.)
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However, if you do this without “Keep Moving” orders, you are relying entirely on the enemy coming after you. (Or rely on, er… brave, valiant, “Picket Captains”…)If the enemy doesn’t come at you, you will never enter weapons range to shoot them 
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If you do add “Keep Moving” orders, then you can be sure that your ship will be in firing range at least part of the time, BUT, you will also be out of firing range part of the time as well. As Aeson mentioned, this reduces your DPS, but might be helpful as it gives you a chance to heal if you need it, but also runs the big risk of your ship wandering into weapons range of other enemy ships that it’s not currently targeting, which kind of defeats the whole point of setting orders to stay far away from the enemy to begin with 
Perhaps having separate “engage” and “retreat” distances would be too cumbersome, but I still kinda wish it automatically made them the same value, instead of retreat always being half of engage for some reason 
Apologies for beating a topic to death, but it has really caught my interest since learning that engagement orders do not work they way I always thought they did. Well, at least I feel confident I actually understand how the orders really work. Now to figure out how to set them in way that makes me not lose 