Why would a ship with a speed of 10 get to move on day 2? Oh wait. Day zero is the first day. Is that it?
In this particular case the star destroyer had a potential move of 18, but as you say five of that was emergency propulsion. I'll assume you are correct about the way emergency propulsion delays to the first normal day of movement, you've been right about everything else.
But in this case it doesn't really matter because the emergency propulsion comp had been expended already on a previous turn. So the fastest that ship was going to move on this turn was 13.
But shouldn't a ship with move of 13 still move the day before (on day 1, the second day) the ship with move of 10 (On day 2, the third day)?
EDIT: I can confirm through testing you are correct. Speed 10 ships and speed 13 ships both move on day 2. And speed 18 ships move on day 1. I just don't understand it completely.
So here we have found a concrete and significant reason to hang on to those old early game escorts and frigates. Retrofit them with the fastest engines you can and stick them in your important fleets so they will have a chance to escape the star destroyer traps late in the game.
The gamey part here really isn't that some fleets can escape, it's that only those with an arbitraty lower ID# ship in them can. It's actually not all that extraordinary to think a fleet sitting on a warp point at the periphery of a system could escape being caught in the blast of the sun blowing up.