I removed the LED's and 100ohm resistor at the emitters of the transistors and now the relays sound like they are clicking appropriately in sync. So the lack of appropriate current appears to have been the culprit.
I suspect that you had a circuit like
12v -- COIL -- TRANSISTOR (C, E) -- RESISTOR -- LED -- GND
Ignoring that raising the emitter above ground isn't very common, lets do some basic analysis.
The coil of your relays specify a current of 30mA at 12v to trip, so we can use Ohm's law to work out the resistance, 400 Ohms.
Let's for the sake of argument just say that the Collector to Emitter resistance is effectively Zero so we can ignore the transistor.
Add in your 100 Ohm resistor, you now have 500 Ohms over 12v.
Let's assume your LED has a forward voltage of 2v. If you started with 12, and your led is eating 2 of them, how many are left. You now have 500 Ohm over 10V.
How much current is flowing, using Ohm's law, 10 divided by 500 = 20mA at the best theoretical case. That might be enough to trip, or it might not, it's well below the specified current either way.
If you put your resistor and LED in parallel with the relay coil instead of series, you will give the relay coil the current it wants, and your led too. (Assuming that the base resistor of the transistor, and the transistor itself, is appropriate).