Creating an low current negative voltage
Get a 15V buck regulator.  You'll either have to drive a push-pull from the switching line, or since you don't need much current you could use a controller with no external transistors.  The point of this modification is to invert the switching pattern.

Otherwise, you hook it up exactly like a 20V-15V buck controller, but connect the ground to -15V and the output (and sense) to ground.  The controller will happily give you your -15V from 3.6. while happily thinking it's bucking 15V from 18.6V.  Usually far cheaper than an off-the-shelf inverting switcher.