You could raise voltage and decrease current by putting several LEDs in series.
For example, say, if the dropout voltage of the LEDs is 3V, then you can power the whole thing from, say, 15V, having four LEDs in series and a resistor to limit the current (for 20mA that would be 3V (remaining from 15-4*3) / 20mA = 150 Ohm). Then you have 25 such bundles in each group leaving you with 500mA a group, 1-1.5A altogether. (Same power consumption but easier to handle, e.g. cablewise.)
The whole group can then be switch with an N-channel MOSFET driven by a microcontroller. When pin is low, LEDs are off, when it is high, they are on. (High = well above FET's gate threshold voltage, but that is usually around or below 1V for the FETs that are rated for 1-2A.)
If you have 3 pins on the microcontroller for this, you don't need to multiplex.
Don't forget to:
- Add a pull-down resistor to the gate of the MOSFET to have everything turned off when the microcontroller is not driving the pin (e.g. when powering up).
- Leave enough remaining voltage at the LEDs for the resistor to be at least 100 Ohm, so noise/variations in input voltage, dropout voltages, resistor values, etc. don't show.