FTL devices don't have to "criss-cross" for you to be able to create causal loops. And even if you don't have any causal loops, other violations of causality violate thermodynamics. It's not as if if you've solved the problem of causal loops--which as far as I'm aware, no one has done without postulating a preferred frame of reference, which is basically rejecting Relativity outright--then you're off the hook. All violations of causality are going to make most scientists shake their heads. And, if it is infeasible to accelerate an FTL drive up to speed, then the point is moot for space travel or communication.
By 'criss-cross' I mean that your FTL devices in different reference frames need to repeatedly get close enough for causal contact. Is there another way to make a loop using simple FTL devices?
And I might not have been clear enough on acceleration. I meant you might be able to construct a device capable of FTL transport, but it might be far harder to traditionally accelerate this entire device to high speed. The FTL isn't moot, but if your FTL is only 5c and you can't accelerate your turned-off FTL device faster than .1c you're not going to make any loops with it.
In other words, in this scenario, there isn't a preferred frame of reference per-se, but there's no way for such a large and complex construct as an FTL device to get far enough away from the galaxies' default reference frame.
You might be able to cook up something, but I doubt that it will be any more plausible than positing a preferred reference frame.
Personally, I think that supporters of FTL should stick with subspace and run with it. And, hey, the author of the FTL faq even wrote a whole subspace faq too.