Did your simulation specify ESR for any of the caps?
Transient simulations don't do noise, so the residual level is not representative of actual noise. TL431s are usually in the 70uV (0.1-10Hz) RMS range, I think.
The two 470uF caps in parallel utterly dominate above maybe 200Hz, assuming their ESR is actually quite low (real electrolytics may be in the 1-10 ohm range, which is comparable, but not dominant to, the TL431's low frequency performance).
Note that it's not generally recommended to utterly swamp a regulator with huge assed capacitors. Regulators work best when they "have room to think", so to speak. Also, marginal values (like 0.01-1uF) cause oscillation. So you're almost as well off with no capacitance at all, as with too much. The main difference is at high frequency.
For low noise and high PSRR, I would suggest adding an RC filter or capacitance multiplier before the bias resistor, and one after the regulator if acceptable (any load will cause a DC voltage drop on the resistor, which can be compensated by tweaking the feedback loop... but that needs a few more components besides).
You can also replace the bias resistor with a current source, which will significantly increase PSRR. High frequency performance will be limited by the transistor's Ccb figure, but by then, ferrite beads will be enough to play clean-up.
Tim