Pick the Rod. Put the burner in the staff and the ground, not in the snake count. Never draw the Man.
1. The Rod, on purpose
A physician's peers read the single serpent as "knows the history". The caduceus reads as the stock-logo default. For a practice whose whole pitch is we actually know things you don't have to explain to us, the correct symbol is itself a credential.
2. But Hermes is the burner god
Commerce aside, Hermes is the patron of travellers, boundary-crossers and tricksters, and he guides souls through the dark. That is the most playa of the Olympians. So the caduceus is not banned here; it is the knowing wink, the variant you make once you have the Rod. Two serpents as two dust devils is the wink at the wink.
3. The staff carries the joke
Rebar bent into a candy cane. Rebar under an orange mushroom cap. A torch. A tent stake in cracked playa. Each is instantly legible to anyone who has pounded a stake at 2 a.m. and invisible to anyone who has not. The snake stays a snake.
4. The ground carries the place
Flat horizon, distant Calico-style ridge, low sun, cracked polygons. Desert without a cactus. A pentagon echoes the trash fence; a horseshoe of concentric arcs echoes the city plan. Nobody outside the fence will notice; everybody inside it will.
5. The Man is off limits
Burning Man Project registers the Man symbol, "Burning Man", "Black Rock City" and more, and bars any commercial or promotional use without written permission. A practice is commercial. The knob-and-wings silhouette that happens to look like a figure with arms up is fine; a stick figure is not.
6. The image models have the same bug
Asked for a Rod of Asclepius, Grok drew two serpents in 11 of 16 first-round renders, and in 6 of 8 even after "exactly one snake, no wings" went into the prompt. The machines default to the 1902 mistake too. gpt-image-2 got it right unprompted, every time.