The load is an infrared lamp for a health sauna.
In that case, just rectify and big caps. The voltage will be about 325V. Heating elements can usually handle that. If you can't afford to try plan B AFTER plan A has failed, just using them on 325V is plan A.
Plan B is to put 1.5 in series, or maybe 2, but then you might have to increase the number of lamps used because they won't reach rated power.
Remember, as the voltage is increased linearly, the power dissipation in a resistor goes up exponentially, doubling by every factor of √2, so 325V would result in double the power dissipation in a resistor, compared to 230V, which will quite likely blow it up.
Edit: To REALLY approach the "requirements" I'd use a transistor in "linear regulator mode". Simply make the base voltage with a capacitor that should stabilize to "just below the lowest voltage on the caps in the last cycle". This can be done with a diode. Also you don't want it to take a few hundred cycles for the voltage on the cap to reach that 325-10V. Then the power transistor will be blown. So add a zener to make it at least 10V below the actual peak voltage. Could be a handfull of components.
That's still a massive amount of power dissipation in the transistor. Forget using a BJT because it'll exceed the safe operating area. MOSFETs are more reasonable, but check the data sheet.
Perhaps a large inductor in series with the bridge rectifier + smoothing capacitor, could be used to reduce the output voltage to 230V. It will also have the positive effect of reducing harmonics and improving the power factor.