I'm a fellow circle-pacer. If I'm particularly agitated, it will be on tip-toes, slowly bringing the posture lower until I have "wound-down" and can put my heels back on the floor. And it is always anti-clockwise (not sure why that is, maybe my left leg is just shorter!).
When I can't do that, I like to scrunch up my toes until it hurts, do circles with my wrists or ankles, or press my arms tight against my sides so that my elbows are jabbing into my torso. I always get shoes that are a bit too big specifically so that I have room to scrunch my toes - it's a good stim that I can use in company without it being noticed!
And when I have a beard (most of the time), I simply cannot leave it alone - it was the first thing that the person who did my autism evaluation noticed about me!
Ezra's mention of humming interests me too. I only do that on a very specific occasion - when there is a machine or something else in the room that is also humming (like mains hum or a motor running). I like to try and get the pitch of my hum so that it's just a little detuned from the surrounding noise, generating beat frequencies. I like playing with that kind of sound in my music software too, so I think it's more the detuning that I get off on rather than just the humming as a stim - I wouldn't do that any other time (unless when I was too young to remember).
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When you are fighting an invisible monster, first throw a bucket of paint over it.