Done!
I used some male and female jack connectors in an ABS box that are just connected to the PSU, so each port can provide the 6V 300mA that the PSU is designed to provide.
I then did as you suggested, and have soldered the resistors in series to the positive side of the cable going to each line. I heat shrinked the whole lot.
I considered putting the resistors in the ABS box, but then if a line were plugged into the 'wrong' port, it would receive the incorrect current/voltage. So this way, any line can be plugged into any port. I figured human error should not be ignored. I did a quick google, and it seemed to suggest that heat shrinking 0.5W resistors would be perfectly safe as in this particular application they aren't drawing anywhere near their max load.
Here is a pic of the box (Yes, I know the wiring isn't the prettiest, but it's definitely secure and soldered well):

The final values were:
Line 1: R39 + R33 (in series) both 0.5W
Resultant Current: 45mA
Resultant Voltage: 2.85V
Sufficient wattage resistors? Yes: I x I x R = 0.145
Line 2: R82 + R10 (in series) both 0.5W
Resultant Current: 35mA
Resultant Voltage: 2.84V
Sufficient wattage resistors? Yes: I x I x R = 0.112
Line 3: R82 + R10 (in series) both 0.5W
Resultant Current: 35mA
Resultant Voltage: 2.86V
Sufficient wattage resistors? Yes: I x I x R = 0.112
Line 4: R39 + R33 (in series) both 0.5W
Resultant Current: 38mA
Resultant Voltage: 2.67V
Sufficient wattage resistors? Yes: I x I x R = 0.103
Note: Line 4 is the longest wire (and 15 LEDs). I assume this is why the mA and V readings are lower. I suppose I could reduce the resistance on that at some point maybe try a single 68, but they are sufficiently bright for now.
So what's the verdict? Did I do ok? Is it safe to heat shrink the resistors? Do the values look ok?
Edit: I am considering doing something similar for my sons bedroom (he has a secret den with a lot of battery powered LED lights and it would be great to have them hooked up to one plug that is voice controlled) so any input on the safety and/or appropriateness of this would be greatly appreciated
