Also check the optocoupler, the side closest the top when looking at the photos.
By my estimation, the current required to toast that resistor would have had to pass though the optocoupler, (edit see below, probably not)
It should measure as open circuit or very high resistance. If it has failed "open" it will be hard to establish from a simple resistance measurement. In circuit it should measure about 270K due to the resistor across it. If it's a low resistance, the optocoupler is shot too.
That would be very interesting because it's certain that the optocoupler would have been OFF if the output was shorted. For it to turn on, the output has to rise significantly above the zener voltage, and it's the optocoupler that turns off the regulator to allow the voltage to fall. It is possible that it failed after the short was removed due to damage which caused the output to go excessively high.
I would recommend drawing out the circuit and working from there. I have done part of it, but I had some stuff upside down so I've thrown it away in disgust
The output looks unusual too. It looks to me that the diode on the output must be marked back to front. Check out the capacitor orientation, the zener orientation, and the +/- marking of the output.
Then again, maybe I need more sleep.
edit: or both transistors. (That was the part I had upside-down) The opto may not have been involved.