There's (theoretically) a way to get around that, though it involves an entirely different approach. Unlike actual particles, the fabric of space can travel faster than the speed of light, so if some way can be found to move a bubble of space around the ship, then FTL travel can be achieved without inertia (since the ship would be stationary from its own frame of reference).

Of course, that assumes that tearing bits of the fabric of space up and moving them around doesn't cause any problems.