Nice! FYI, you can use those USB phone-charging battery bricks for a nice compact 5V output in those sorts of projects. I think TSA-approved ones run up to 100Wh, and they're easy to recharge.
Most of them will cut power after
a minute of so if you don't draw more than like 100mA of current, but that shouldn't be a problem with 350 LEDs. It'll save your Arduino's voltage regulator some grief, too :)
Ah that's a great idea for the Arduino itself! My board burnt out because my independant battery source for the board didn't work out so I wired it in parallel with my batteries (3x8 AA batteries in series put through a voltage adjuster). I'll be buying one!
Most of them will cut power after a minute of so if you don't draw more than like 100mA of current, but that shouldn't be a problem with 350 LEDs. It'll save your Arduino's voltage regulator some grief, too :)