I've decided to use these net lights on the same 30V - 31V DC supply as the Big W strings.
For the white LED set, I added a 51 Ohm 0.6W resistor in series with each of the channel wires. These values gave me approx 70mA current draw per channel from 31V DC.
For the multicolour LED set, I added three 15 Ohm 0.6W resistors (to get me 45 Ohms 1.8W) in series with each of the channel wires. These values gave me approx 120mA current draw per channel from 31V DC.