That was an interesting paper, but I'm having trouble with the concluding paragraphs. Is the argument against the grandfather paradox essentially "You can set up the mechanism to create the grandfather paradox, but it won't actually work the way you think it will?"
Bob's argument is (more or less) that it's easy to set up a thought experiment in which you imagine setting up closed causal curves, but that the devil is in the details.
Earlier in the paper, he argued that the new physics will still have its own causal structure, in a well-defined sense involving initial conditions and differential equations. If you start with complete and well-behaved initial data, his argument is essentially that the state of the system will always evolve forward in time in a consistent way (and in particular, there's no way for closed causal curves to arise out of nowhere).
So those last paragraphs that you're asking about attempt to interpret that conclusion in the context of a thought experiment aimed at creating a grandfather paradox. Geroch's answer is to say "the details will depend on your precise model, but the math makes it unavoidable that something about the model will make your plan impossible". Maybe the experimenter's normal-matter hands just can't ever move fast enough to push the special fluid past light speed. Maybe FTL-fluid is explosive when it comes in contact with normal matter. But the ultimate mathematical conclusion must hold.
(I won't swear to have worked through every step of these arguments in detail myself, but Bob Geroch is a world-class expert on this sort of thing. The one caveat that I'd add is that I think his arguments here are classical, and that bringing quantum mechanics into the mix might change things. It's possible that it would only change things in topologically disjoint sectors within a general-relativistic spacetime, but something like that might conceivably escape his premises.)