PaulRB:
Normally, multi-digit 7-seg displays have common anodes and common cathodes and there is no choice but to multiplex. A 3-digit display would have 11 or 12 pins. Does your display have more? Like 27 pins for example?Also you say that the digits are 1.2" high but you need to drive them with 3.3V. Large digits often contain two or more LEDs in each segment, meaning 3.3V will not be enough to drive them. What is the forward voltage of the segments in your display?
You also say you want to drive them with 10-20mA per segment. Is this to achieve high brightness, for outdoor use for example? If so, this will be difficult to achieve if you need to multiplex. Multiplexing lowers the average current and therefore brightness. Multiplexing by digit would result in a 1 in 3 duty cycle and would lower the average current and brightness to one third of your target. This can be compensated for by increasing the current and over-driving the display, but if you don't have data sheet, you don't know if that's safe to do without damaging the display.
Also, even at 10mA per segment, you would need 210mA at 3.3V if not multiplexing. This is close to the limit of what the Nano's regulator can provide. Even large batteries will be quickly drained.
So... please provide much more information, if you truly want our help. A link to the data sheet for the display, if you have it, or any codes printed on the display to allow a Google search. And details of the batteries to be used.
They are individual 7-segment elements, each element has 10 pins, so 30 pins total. The displays are listed as Vf=3.3V and If=20mA max. There are no markings on the devices. I determined the pinout at trial-and-error. Power is planned to be from a 2-cell 18650 battery pack (rated 4400mAh).