No that’s ok. Because in the inverted augmented scale you don’t have the maj7 (=11) note and you take the 6 instead in order to get the chord with 4 notes. But then this collides with the #5. I tried to play some versions on the guitar and it sounds best if you take the 6 into the bass, like C6#5 = a-e-#g-c. In other words, use an inverted version. As numbers this looks like [-3, 4, 8, 12]. But you can keep the [0, 4, 8, 9] version if you want maximum dissonance.
EDIT: the [-3, 4, 8, 12]. is basically the same as a minormajor7 chord. So C6#5 inverted = Am major7
EDITEDIT: should read -3 instead of -2