I don't think it's a good idea to operate those zeners at such low
currents, you're at the knee and lucky to be within 20% of nominal
voltage, and SPICE doesn't model zeners in that region of operation well
enough to be trusted...If you don't like the crummy 20mA bias, go with a
'431, at least you will know what you're getting and you can derive the
majority of the bias from the regulated output, using the unregulated
input for start-up only, ending up with enormous ripple rejection. I
went with the 5V6 1W because it's popular, readily available, cheap,
takes the 60V load dump, and good enough...
I think the CMP or CMH zeners are characterized at 250uA, with a
dynamic impedance around 1K3. The spice model showed the biasing
kicking in around 4V with the 2K7 load resistor.
My own version uses a low power 431 and a steering diode instead of
the two zeners, but I like the simplicity of your arrangement for this
lower power app, with apparently reduced compensation issues. The OP
only wanted 3mA out. Interesting to see effects of capacitive loading.
I don't think there's a load dump issue, except possibly for the
transistors.
Taking all models with a grain of salt, this circuit shouldn't raise
breadboarding issues with the novice.
RL