Hi Stuart
You seem to be using the 14 pin chip which I have never used.
The link that someone has made work seems to call up the circuit you need but in the 8 pin form for 2907.
The 2917 has an internal zener on pin 6 for the 8 pin chip or pin 9 for the 14 pin version.
It is this pin 6 or 9 depending on the package that must have the 470 ohm limit resistor ( not needed for 2907 ). You have connected pin 9 to supply and that will be why it gets hot.
If it really is a 12v LED with its own limit resistor ok if it is an ordinary Led it will also need a limit resistor 0f 470 ohms to 1k.
I have tried to follow your description of the circuit and there are a couple of things I dont agree with.
Pin 3 and 4 joined have a 10uF capacitor to ground and a variable resistor that should be in the 100 to 220k region not ohms.
When you say pin 4 is grounded, I think you mean pin 5.
On the 8 pin circuit it shows 10 k resistors from pin 7 to pins 6 and 8. these are needed to get the reference point of the op amp in range. You can replace with a 10k pot with slider to pin 7 to alter the frequency in addition to the variable on pin 3/4 but the range is limited, it has to stay near mid volts.
For your 14 pin amimal it looks as though you need 10 k to pin 9 and pin 11 to have the same thing.
The 14 pin data sheet seems also to indicate that pin 12 should be ground but I am not sure.
To start with I would omit the 500k latch resistor from pin 8 to pin 10. Without it the LED will not switch cleanly from on to off but it removes one possible source of trouble.
I hope this is enough to get you working.
Flux