Lucky you didn't let the magic smoke out of the power supply supervisory circuitry .... That could well have let the magic smoke out of Everything else connected to the power supply too. It's usually the 5V source that supervises everything else, If the math behind the transformer design is right all will be fairly well controlled by controlling the 5V high current output. As to Capacitors I'd use the biggest one that fit 10KuF or .01F would not be out of line... At least on something I would build. a 10,000 uF cap isn't really very big even at 35V working voltage.
Doc