Make a stacker regulator. Generate an isolated 3v DC supply (ie a forward converter), and stack it on top of the 12v supply. Run the regulation control from the combined output to maintain 15v out.
It's just like putting a 3v battery in series with a 12v one, and is very efficient as the 12v portion fo the supply is delivered at 100% efficiency and only a small percentage of the supply is done by the SMPS. Total efficiencies can easily be 95%+.
And these days I don't think anyone still does stacker designs like this except me.