The voltage drop at 240 volts is irrelevant to the situation, as the circuit will be capable of 120v load on one side, and needs to be "engineered" to handle that situation. It is quite possible that the user may plug every piece of equipment they have into the same side of the circuit. Very few people go around thinking, "this is the A side and that is the B side, and I plug this in A and that in B and we'll be even". I actually did just that with my lighting multiwire circuit, but it was a one time thing and easy to do, the top half of each receptacle being marked with a big red A and the lower half being marked with a ********* B (at each fixture) which corresponded with the colors of the wire supplying the receptacle top and bottom and the buss bars of the panel board as marked on the panel diagram on the inside of the door.
If possible the OP needs to split the whole thing into two different runs, using two double pole circuit breakers (ie "240v breaker") instead of just one as you propose to use. Somehow you really need to shorten the runs, or up the wire size for part of distance.
What the OP is proposing is known in the NEC as a Multi-wire circuit (aka "Edison circuit") which takes advantage of the alternating current to share the neutral with two different hots drawing from opposite busses of the panelboard. Current NEC requires in most circumstances that the breakers used have the handles tied together so that they will both trip should one circuit overload. This provides safety to anyone working on the circuit in that it assures that ALL power is removed from the boxes where the receptacles are mounted. It also assures, due to the alternating stab design of circuit breaker panels, that the two hots are indeed opposing "phases" of the panel. One other thing to be especially aware of when running a multi-wire circuit, is that the neutral must be continuous and uninterrupted by the removal (either temporarily or permanently) of a component of the circuit such as a receptacle. This means that you cannot run the neutral to one white/silver screw on the receptacle and come off the other white/silver screw with the neutral continuing to the next box. Instead, you need to take the bare ends of the two neutrals (in and out of the box) and add a third wire, a pigtail, and wirenut all three of these together. Then the short pigtail is attached to the receptacle. Thus, when the receptacle is removed for maintenance or replacement, and the pigtail is disconnected, the upstream and downstream neutral wires remain connected together.
Charles