But the introduction of FTL lets Q interact with you, which means by definition Q must be within the cones.
The cones are defined by c. Q cannot interact with you because there's no such thing as FTL. If it could interact with you, then it will still lie outside the cone, and you would still be violating causality. Don't try to argue the point with me, do your own damn research. There is no question that FTL is time travel in a universe where special relativity holds true.
http://www.phys.vt.edu/~takeuchi/relativity/notes/section10.html
http://en.wikibooks.org/wiki/Special_Relativity/Faster_than_light_signals,_causality_and_Special_Relativity
http://physics.stackexchange.com/questions/196/what-are-some-scenarios-where-ftl-information-transfer-would-violate-causality?rq=1
http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html#18
There are lots of arguments against time travel but this isn't one.
The past does not exist anymore. The future has yet to exist. There is no infinite regression of universes in the past and future directions to which you can travel. That's preposterous and it should be obvious why.
You have been taught to think of time as an axis much like spatial axes, yes? Unlearn that. It is useful in modeling physics but it has no basis whatsoever in the real world. No evidence whatsoever to support that way of thinking, and in fact plenty of reason in special relativity to find the way of thinking highly suspect. Time is a human measurement of change. It is a human way to interrelate remembered events with present events and with anticipated events. Without change, time has no legitimacy. Time simply is not a regression of past moments and future moments through which we travel.
But this can't be true because of Bell's inequality, which means something is being sent faster than light.
True, not every interaction in physics appears to be local. However, every meaningful interaction - that is, one that carries information of any form, including the transportation of matter - is limited by locality. Bell's inequality does imply a superluminal interaction but it does not imply FTL travel or communication, because the interaction cannot possibly be used to convey meaningful (i.e. nonrandom) information.