LED spot flickering problem
This is your problem:

We have them connected in parallel with a driver that outputs 15-34V at 1500mA. 


That is a constant current driver that operates between 15 and 34Volts.  Your lamps operate at around 12V.  The current regulator can't operate that far down, and so isn't doing its job properly.

For this to work right, you would need to put the lamps in series.  That won't work for all four, though, as neither of your regulators can go up to the 48Volts that the four lamps in series need.

Since you have two power supplies at hand, try this:
Wire two lamps in series to each driver.  That gets the required drive voltage into the middle of the range for both power supplies, so the regulators should work properly.



It is in general a bad idea to put LEDs in parallel because the voltage at which they turn on can vary a little bit.  The LED that turns on at the lowest voltage gets all the current, which could cause the LED to burn out.