Jazz III users: Does your thumb/index finger hit the string when you’re picking? [QUESTION]

For Jazz III users, or anyone who uses similarly small picks:

I just switched to the Jazz IIIs and boy is it small! Even for me with skinny fingers, I’m having a hard time getting a stable grip on this thing. I haven’t played that much with it yet so hopefully it’ll get better with time.

Anyhow, I’m noticing that with so little sticking out, my thumb and index fingers often end up rubbing the string that I’m picking. Is this problematic? Or does this just mean I need to up my accuracy?

EDIT: I forgot to mention that I’m already using the max-grip version

PS. I’m curious about trying out the larger Dunlop Flow’s one day if this doesn’t work out.