Sorry for being unclear.
Rather than running a 120V circuit consisting of a single ungrounded (hot) conductor and a single grounded (neutral) conductor, I am suggesting running two 120V circuits with a shared neutral, consisting of two ungrounded conductors from two different supply legs and a single grounded conductor. This is called a multi-wire branch circuit (MWBC), the benefits and issues of which are regularly debated. I am not saying that this _is_ the best circuit to use in this case, simply suggesting that it be considered.
In the ideal 'balanced' case, no current flows on the neutral, so that there is no voltage drop on the neutral. In the case of two legs from a three phase system, or in the case of harmonics, there will be voltage drop on the neutral, but it will be reduced from the single circuit case.
Rather than 8A on a single circuit, you have 4A on each of two circuits.
The net result is that the length of conductor over which you consider voltage drop is reduced, and the current flow causing the voltage drop is reduced. The benefit of the MWBC is so large in this case that the voltage drop is lower if you use 12ga conductors in this configuration than if you use 10ga conductors in a single circuit configuration.
4 #12 conductors contain less total copper than 3 #10 conductors. (Remember the EGC!) So the wire is probably less expensive even though you have more conductors.
The cost adder is that you need a double pole breaker, and double pole switches.