You don't have to find a Darlington, you can make one, pick yourself a pass transistor and then add another 'driver' transistor, have a look at the Ham Jumbo PSU, that's pretty much a classic Zener regulated, Darlington pair based PSU.
As mentioned earlier, if there's no load on the output then the current through the Zener will be maximum, limited by the series resistor so that's why your Zener got hot.