Cause from what I've learnt with wiring PC fans to AC-DC adapters is that too many amps, POOF.

Too high of voltage allows too much amperage to pass through a device. However if the voltage is within rating for the device, the device will limit the current on its own. So you cannot hook a 5v fan up to a 12v power supply or you might put too much current through and blow it.

Power supplies don't push the amount of current they are labeled at. The label simply indicates the maximum they are capable of pushing if the circuit allows it.

The amount of current the circuit allows to be pushed through it is Voltage = Current*Resistance. So Current = Voltage/Resistance where R is an inherent value to your light. LEDs are a tricky case where resistance isn't a static value, but varies non-linearly so the easiest way to determine the actual current you are pushing is to measure.

You know at 7V they allow 700mA through, so at any lower voltage they will allow less. At 3V it is likely much less(possibly in the 350mA range you are looking for).

Alright so that series circuit with only 11 works, but if you wanted to go all out, you could run the 4 lines with 11 LEDs each correct?

I would measure the current of a single line, and make sure it is actually 350mA. It could just as easily be 400mA, then you would be trying to draw 1600mA from you're power supply, and possibly blow it.