I don't think I will need any resistors at all for the TLC5940.
Should I ground the 12V supply to the arduino?
I have read that I need to get rid of the IREF 2.2 resistor and that makes sense to me because the higher voltage I am trying to use.
The LEDs have their own resistors already built into the strips.
The TLC5940 can operate with a 12V supply to the chip. In fact it will operate up to 17V.
This is incorrect!
The datasheet says Vcc should be 3-5.5v with an absolute max of 6v.
the maximum combined current that the chip can sink is 120mA.
Also note that whilst each output channel can sink 80mA of current, the maximum combined current that the chip can sink is 120mA.