Because the current you can get is 500mA per channel, but the thermal considerations are such that it will overheat if you drive a total of about 650mA for the whole chip. So this is way down on the current capability needed for this project, which Is 600mA per bulb.
For the ULN2803 its given a total maximum current of 2.5A, but it really won't be enough, especially with 2 bulbs per channel.
Then the variant with transistors IRLML2502?
That's only one limit given in the datasheet.
If you combine that with saturation voltage and thermal resistance,
then the chip will be 250 degrees C.
Leo..
If you want a walk through these calculations, see this page I wrote for the very closely related ULN2001 device.
Power Examples
I would suggest finding out what parts you have to work with, you stated it was limited and supplied locally. With that information you can get a much better answer. Are the parts mentioned even available?
Only the specific Arduino board will be purchased locally. The question was about extending the outputs and switching higher voltages, regardless of which board I got. I've already ordered everything else, thanks to the help I received above. 
Unsure if this is allowed, but I wanted to share where this circuit ended up. Thanks for all the help!
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