Solo Harmonica Study 1, ex. 1.10

For this exercise, I'm having a hard time trying to get a smooth 1 - 2 draws (tongue-switching) at the beginning of the pattern, 2 draw tends to lag. And even worse adding the accentuated transition from the last bar "(12) | 1 2".

I have found a horizontal jaw movement that seems to make it easier: for 1 draw, my jaw is slightly to the right, and while tongue switching for 2 draw, it gets slightly to the left (following the tip of the tongue). This seems to give me a quicker 2 draw. Then, straight jaw the rest of the bar, then the transition to 1 draw seems more "percussive" somehow by moving the jaw again to the right while putting the tongue.

It seems to work, but I wonder if it's ok to have horizontal jaw movements, or if these are parasitic "cheating" movements that hide the true reasons for the good results (that I should then seek to isolate better).