I would certainly defer to your much superior knowledge of physics. Mine is only that of an MIT student who was thoroughly indoctrinated with Special Relativity as part of MIT's general science education, and who sat in on an undergrad course on GR taught by cosmologist Max Tegmark.
If I understand Bob Geroch properly (much of his paper is Sanskrit to me, but I think I understand the parts that are in English), he acknowledges that FTL particles would seem to allow you to set up "closed causal curves" (i.e., violate causality in a way that would allow you to try to generate a time paradox), but he asserts that you would never actually be able to achieve this goal due to something like the "Novikov self-consistency principle", although he doesn't mention this principle by name.
This is similar to the position that many physicist think about the existence of closed time-like loops in GR. Sure, in some sense they are possible, since GR shows you how to set them up, but something like the Novikov principle would either prevent you from setting one up or from doing anything nefarious with one.
So, if I understand things correctly, Geroch's claim doesn't really different too much from assertions that I made elsewhere in this thread, that sure you might be able to build an FTL drive, but if the universe lets you do this, it's not going to let you make good use of one, like, for instance, creating an FTL space-liner fleet, because if it did, you'd generate a time paradox soon enough. Or if the universe were so kind as to let us do that, we'd end up finding ourselves in a very strange world where Novikov's principle was mucking with our daily affairs in a very creepy manner.
I've admittedly not worked through Geroch's paper thoroughly myself, so I won't make strong claims here. But based on my understanding, I'd say that his assertion is a bit stronger than what you're suggesting here. He's not just giving a sort of meta-argument that "the space-time manifold of the universe must be consistent, so some mysterious effect will always stop you from killing grandpa".
Rather, his point is that your second theory (the one that you're adding to standard relativistic physics) has already been assumed to be causal when taken on its own (it must have a well-defined initial value formulation: that's one of his postulates). What he demonstrates is that putting the two causal theories together will still preserve causality. So when he says that you won't be able to use standard SR tricks to create closed causal curves, he really honestly means that any possible arrangement of the matter/energy content that could do that would be forbidden by the fundamental laws of the theories you're using. (Not just that it "wouldn't happen to work out".)
To phrase it yet another way, Geroch would say that you could not build a time machine in such a theory, not just that you couldn't use it to change the past in a meaningful way.
If I understand Bob Geroch properly (much of his paper is Sanskrit to me, but I think I understand the parts that are in English), he acknowledges that FTL particles would seem to allow you to set up "closed causal curves" (i.e., violate causality in a way that would allow you to try to generate a time paradox), but he asserts that you would never actually be able to achieve this goal due to something like the "Novikov self-consistency principle", although he doesn't mention this principle by name.
This is similar to the position that many physicist think about the existence of closed time-like loops in GR. Sure, in some sense they are possible, since GR shows you how to set them up, but something like the Novikov principle would either prevent you from setting one up or from doing anything nefarious with one.
So, if I understand things correctly, Geroch's claim doesn't really different too much from assertions that I made elsewhere in this thread, that sure you might be able to build an FTL drive, but if the universe lets you do this, it's not going to let you make good use of one, like, for instance, creating an FTL space-liner fleet, because if it did, you'd generate a time paradox soon enough. Or if the universe were so kind as to let us do that, we'd end up finding ourselves in a very strange world where Novikov's principle was mucking with our daily affairs in a very creepy manner.