Technically you still can't distinguish acceleration from gravity - they are, in fact, one in the same. The simple direction difference between the negative and positive masses accelerations are not qualifiers for discrimination. There is no way, in a single reference frame, to distinguish the negative and positive masses - i.e. whether the earth is negative or positive mass and the object in question  is positive or negative. Further, the magnitude of the acceleration should be identical for each object.

I would suggest reading up on Hawking's idea (in his universe in a nutshell book) that mass energy + gravitational energy = 0. In essence, you can create all the matter you want, as long as it has gravitational pull which he regards as a negative energy. If this is the case, then there could, in fact, be negative mass with positive gravitational energy, which behaves in an opposite manner. I would presume that annihilation due to matter-antimatter interactions would have gravitational energy considerations as well - but in any case, the mere fact that negative mass would accelerate in a different direction in a gravitational field does not in itself preclude its existence, especially since gravitational laws were formulated without accounting for this eventuality.