The annoying thing about this is that it's bloody hard to find a propulsion method that properly illustrates their technological advantage without resorting to some sort of agrav or something of the sort.
Oh, it actually is very simple. Try this: "we do not understand the underlying physics completely. whatever it is, it lies well beyond every modern theory"
And yes, I understand the difference between sci-fi and boring reality, but even sci-fi must be self-consistent and go in accordance with the current science. So if you want to provide an explanation on some tech, let it be correct. If you can't - just provide nothing, like you do with antimatter.
About FTL I also have a complain. In "alien origins" you say "FTL violates relativity", which is, of course, true, but what you actually meant was "the way the ship pops in violates relativity", which is not exactly true, as we do not know how the ship pops in.
The theory of relativity is too well-established to just say "this ship violates it" and pretend that you are still a "hard sci-fi". But the thing is, that no theory can be "the theory of everything", every theory has it's scope, and you just need to go outside this scope, and limitations of this theory won't apply anymore. Modern human science doesn't go outside relativity theory, alien's - obviously does.
Long story short: when you need to describe something beyond modern physics, do not try to apply modern theories to that, because in that case you'll be bound to the restrictions of that theories. Just say "we do not have theoretical basis for what we see".