To make it most efficient i decided to use 2 switching regulators. One for the 3.3V and one for the 12V. To make life easier the 12V are only 11.3V so a buck converter instead a buck/boost can be used for it.
Both switchers use the same IC, only the component values differ a little bit depending on the output voltage and startup time. The 3.3V start a first and approx. 10ms later the 12V are ready.
Here is the schematics for both regualtors:
The size is approx. 20x20mm²