Hi.
Thanks for listening.
In fact there are many different approaches for a scale like this one. You can emphasize a tonic or not, you can rely on the enharmonic feature of the augmented chords (C+ = E+ = Ab+), you can treat the piece as lineal (melodic, horizontal), you can take advantage of the possible chords that come out from the scale (C, Cm, C+, E, Em, E+, etc...), or even you can think that the basic scale (C, D#, E, G, Ab, B) is a Pitch Class Set (Prime Form (014589) and interval vector <303630>). The most important is to avoid any shadow of major/minor modes, that it, dominant-tonic progressions.
There is a moment when I use all the notes of the scale at the same time vertically, in a sort of pandiatonicism, that's the part that sounds crunchy, I think.
Regarding "I do wonder why you sometimes offset certain of the notes", if you talk about things like the one in the picture below, it's just a matter of texture and anticipation of the motif.