If I move a ship and the final position simultaneously overlaps a ship AND would have it be of the board, which takes precedent? I'm assuming the collision prevents the ship from flying off the board, and it has to slide back to the next safe position, but I could be mistaken.

You resolve the overlap first. You only go off board of the final position is outside the table.

The collision takes precedence. This is actually covered in the FAQ, page 6:

Q: When a ship executes a maneuver such that a portion of the ship would be outside the play area at its final plotted position, but the ship overlaps another ship at that position and finishes its move entirely inside the play area, is the ship that is moving destroyed?

A: No.

...you and your fancy-pants rules references...

The advantage being that you can just edit in my rules reference and then claim the edit was to fix a spelling error, and make it look like you totally ninja'd me.

And now I've exposed @Drasnighta 's dirty little secret.