This question was never addressed:
Even ignoring the neutral issues for the moment, the two line currents would be on separate pathways, and possibly lead to conduit heating.
Yes, not having the current return back through the neutral conductor of its own circuit has a number of issues. They include the possible heating you mentioned, higher magnetic fields from the large circuit loops created (possibly leading to interference issues), and violating a key principle within the NEC, even though it may not be within the domain where that code applies. Some people are apparently sensitive to 60 Hz magnetic fields, but that's something I know little about.
A way to have current return through the neutral conductor of each 120V circuit is to insert a winding from a relatively low voltage transformer that has a 1:1 ratio in series with the 240V load as in the circuit pictured below. This circuit has the same effect as putting the neutral conductors in series with the load, as is the case in normal 120V circuits. The voltage drop across the neutral conductors will be added to that of the line conductors, as it would be with L-N loads on 120V single-pole circuits. The total voltage drop on a percentage basis should be about equal to that in 120V L-N circuit when the same load current is drawn. There will be some drop through the transfomer itself but it should be relatively minor, as discussed below.
The transformer only needs to support the amount of voltage developed across the neutral conductors at terminals N1 and N2 without substantial distortion. It's likely that a 1:1 transformer for 24V would be more than sufficient. And so the kVA rating needed could be less than 1/10th that of isolation transformers necessary to support the 240V load. Even if the voltage drop across the neutrals gets high enough during motor starting, etc. to saturate the transformer, it just means not all of that voltage drop will get put in series with the load. Which is actually a good thing in this situation. The transformer would need to be rated such that its insulation supports 120V to ground.
If the impedance of a 24V transformer is say 5% and the rated current is 20A, then at 20A it would have a voltage drop of 0.05 x 24V = 1.2V, or 0.5 % of 240V. This is the drop you'd get if the neutral conductors had zero resistance. And so the contribution from the transformer itself to the voltage drop should be relatively low.