Seeing how much breaks from switching to stationary player/moving universe could actually be a fun way to start. It's always possible that everything is abstracted well enough that it just works with making the updates to the core calculations. Only things that _change_ an object's position relative to whatever 0,0 is should need to be updated. Once positions are determined each frame, nothing else should be any different, I can't think of any assumptions after that point that would matter.
So you start at 0,0 (2D for simplicity's sake) and everyone else starts at some x,y. Let's say you accelerate along the y-axis and another ship was moving along the x-axis. You would have moved 5 in the course of a frame along that axis, and the other ship moved 10 (arbitrary units). Right now you have a calc that says ok, your new position is 0,0+5. The ship at x,y at the start of the frame is now at x+10, y. Now, you would instead keep your location as the 0,0 reference. So the other ship (to maintain the same relative position to you as before) would not only move the distance along the x vector it was before, it would move along the y vector in the opposite direction, or x+10, y-5. If jumping a large distance in mission that should be accomplishable the same way, whatever vector would have been applied to the player to jump far away, apply that to all the other objects instead, accomplishing the same goal.
TL;DR: Formula should just be to add the opposite player movement vector to all objects in mission and leave the player at 0,0.
Ok, I do see one gotcha. Any code that references absolute coordinates after the mission has started would somehow need to be updated every frame or something, or a vector containing how the player has moved since the mission began would have to be maintained so that any time absolute coordinates are used, that vector would applied, or probably many other solutions that I'm not aware of for a problem like that. But they could probably all be updated every frame just like all object positions are updated, although updating many things that weren't changing before might have a performance impact.