Discrepency with experimental vs. simulation of AC-DC circuit
The problem is your current measurement method and assumptions for load current.

I get I(R1) = 177 mV dc /150 Ω = 1.18mA with a 1K load at 9V out on 470uF cap and 9.7V Zener with Iz=17mA pk using Si diodes.

Since nominal Zener Vz= 9.4~10.6 @ 5mA and Zt is around 15 Ω at 17mA pk 

I used 1k load for 1.18mA average. 
Assumptions for load on mine were different than yours.

Your measurements were:


24.3mA true RMS
12.75mA multimeter


Your assumption on how multimeters work is wrong for AC current.


They assume perfect sine wave and measure peak (or average) then scale down by 1/√2 or √2/π (depending on design) to get RMS. But your current is a complex DC + 50Hz AC sine current riding above this. So RMS current is not accurate. 


To make accurate complex current measurements with cheap multimeters, use a shunt resistor and 10K R with 100uF cap and measure DC voltage.



My Simulation