Among presolar SiC grains found in the Murchison carbonaceous meteorites (average size less than 0.5 μm) are very large grains, ranging in size up to 50 μm. We interpret ⁶Li excesses measured in eight of these grains as being the result of spallation reactions by Galactic cosmic rays during the time the grains spent in the interstellar medium before their incorporation into the meteorite. Derived interstellar exposure ages range from 40 My to 1 Gy, the highest values being consistent with theoretical expectations of interstellar grain lifetimes. Although six grains have almost identical C and Si isotopic compositions, their exposure ages are very different. This observation, combined with low trace element contents, and unusual grain sizes, raises fundamental questions about their stellar sources.