If all of your statements are true then why does the rule in the book say " causes any part of it's base to go outside the play area" neiher the rulebook or FAQ say "causes any part of it's base to end up outside the play area" it clearly says "to go". I'll wait for an official ruling from FFG becaue no the FAQ does not clearly cover this. All page 4 of the FAQ proves is that yes if your ship would end overlapping another and travels back til it is no longer overlapping said ship, but it's base now has any part outside the play area it is treated as "Fleed the Battlefield"
As I think he/I/we have been trying to explain, there's nothing in the rules that says anything about your movement template having any kind of interaction with the edge of the play area (the way it does with, say, an asteroid). As you point out, it stresses in big bold letters in a couple of places that if any part of your ship's base "in its final position" is outside the play area it is considered to have fled (not 'fleed,' btw) the battle.
There's nothing anywhere in the rules to indicate that it matters at all if the template crosses the boundary of the play area, so as long as your ship starts fully in-bounds and ends fully in-bounds, there shouldn't be any problem, at least as the rules are currently written. They could always clarify it in the next FAQ I guess.