You are making a fundamental error by assuming classical kinetics. At .9c, your first interactions would be electronic (ionization), then nuclear and radiative. The complete and initial ionization of all the atoms of 10mg of, say carbon, would be a lot less than 360 GJ. Then you'd have different interactions depending on your hull material, magnetic shielding/Bremsstrahlung losses, etc...

With some complicated magnetic fields, you could probably do something smart to take advantage the different charge/mass ratio of an ionized atom and positron and minimize interaction with a steady/confined positronic cloud. You might be able to annihilate enough electrons of the dust particle to ionize it enough to subsequently deflect it from the ship. Then you'd still have to worry about gamma ray radiation and back pressure and maybe some other interactions.

I don't really know about all of this for sure, just a thought.