How to get a 1.6 times higher supply voltage
The simple solution is to rearrange your LED matrix into 20 x 5 LEDs. In theory strings of 6 LEDs would also do for a 20V supply, but it would only give you 0.8V to control the current and that's too little, a small variation in LED or supply voltage would give a large change in current. So calculate the series resistor (one for each string, it's not on your schematic) as R = (20V - 5 * 3.2V)/(LED current).
If the current is 100mA (you talk about 1A for 10 strings) R would be 40\$\Omega\$. Make that 1W resistors. Total power is 20V \$\times\$ 20 LED-strings \$\times\$ 100mA = 40W.