TIFF is not a good choice for the web. If you use JPG, we can see your schematic without having to download it.
I'd use a 470 ohm resistor. Right now at best you have about a 40:1 ratio of current. But when you are trying to drive a transistor into saturation, the gain drops drastically. Plus, you want to make sure it is overdriven. I use between 10:1 and 20:1 collector current vs base current. 470 ohms will get you around 8.5mA base drive (voltage out of an Arduino pin drops below 5V when you draw current) for about a 12:1 current ratio.
But then you've eliminated that as the problem with a 220 ohm resistor.
What about your 6V supply? Where is it coming from? What is the actual voltage, both without blinking the IR LEDs and while blinking them?
Do you have an oscilloscope you can monitor this with? What does the waveform on the transistor collector look like?
Your iPhone almost certainly has an IR filter, otherwise plants in sunlight will have their color balance messed up. More likely is that, like every other camera with an IR filter, it just doesn't block out all IR.