Several thoughts:
In principle, according to the Everett-Deustch “many-worlds interpretation,” the Grandfather Paradox has little to do with either (a) the timeline involved, or (b) the traveler himself. The common fallacy lies in the concept that only one spatial-dimension is traveled. Realistically, the only plausible solution is that the “time-traveler” is involved in some sort of peripatetic activity (for lack of a better expression) in the multiverse, i.e., multiple levels of dimensional reality are being accessed to complete the theoretical scenario.
As for FTL in Special Relativity, first, we have the EPR paradox. I know, I know: you're saying, “it’s a highly-contested model.” Nonetheless, I re-present it as indication (however subtle it might be) of FTL potentiality.
Further, special relativity doesn't preclude FTL speeds. It forbids an object traveling at v < c from reaching c. If, however, the object was ALREADY moving at v > c at the moment of its inception, theoretically, it should be acceptable in the framework of special relativity (it would not be able to decelerate to < c).