Edit: yup, it's the same every time per browser, but I can have e.g. Edge and Chrome running next to one another doing different things.

Floating point is completely deterministic (as you note by getting the same behavior every time you run the simulation in the browser). I'm looking at the js spec, and there shouldn't be any freedom in evaluating floating point expressions (but overly clever browser vendors may have ignored that and reordered them anyhow).

However, I do know for a fact that the implementations of the Math.sin and Math.cos functions are browser specific,

https://tc39.github.io/ecma262/#sec-math.sin

so that alone will remove any chance at browser independent reproducibility, without additional controls.

Be interesting to see if replacing Math.cos and Math.sin with your own implementation would remove the cross browser dependency.

Btw, spec conforming implementation of Math.sin

  function sin(x) {
    if (   x === Infinity 
        || x === -Infinity
        || x === NaN) {
      return NaN;
    }
    return x;     
  }