How about "omega" as the symbol?
1) It wont bother the physicists as much as tau.
2) Omega has a circular shape which makes it a 'natural' choice for the circle constant.
omega is the symbol of choice for angular frequency, which is very related to pi, as angular frequency = 2 pi frequency (there is another 2 pi for you right there).
That's omega in its minuscule form. I was referring to its majuscule one.
Oh, I assumed that "omega" is minuscule, and "Omega" would be majuscule, just like in LaTeX. That's why I started the sentence with a small letter. I missed your mentioning its circular shape.