@xvrAlright everyone, I am patenting this topology called Prince Charge Pump which can be somewhat described as inverse Dickson charge pump based on my google searches.
After thinking and simulating I realized my previous guess on the topology lacks the charge/discharge control. The 12V rail is fed for some time but then discharged later. I'm pretty bad at simulation but I guess I got something useful:

alternative link for simulation screenshot:
https://imgur.com/a/Ws3JqcSn008: D12_Cathode
n006: D12_Anode (GND of the new topology)
n010: D11_Cathode
n012: D11_Anode (GND of the old topology, the one used in the report)
So please focus on (n008-n006) and (n010-n012) for regulation performance.
I managed to get similar performance from both, so at least my crude simulation verifies the design. One thing I noticed and expected was the need to increase the capacitance of the dropper capacitor in the new design to keep regulation going. I was expecting this because it sees less dV meaning less current, but I didn't expect the difference to be that large, 220nF vs 4.7uF (x21). The final value should be found empirically. At least now the capacitor only sees single polarity of voltage meaning electrolytic caps can be utilized and higher capacitance requirement is no issue. I also decreased the inrush limiter resistor (R1) just to get the time constant or RC well away from the rectified AC period, probably wasn't mandatory but doesn't matter anyway.