Sound a lot like the use of a 'zig-zag' tranformer to derive a neutral from a delta supply. I don't see that it _couldn't_ work, but I bet there are some subtle failure modes that make this a bad idea. However in the below I am just guessing.
For example, in the system you describe I bet loading that puts imbalance on one side could shift the potential of the neutral. How do you ground the neutral of the autotransformer? Since the system is not galvanically isolated, connecting the new neutral to ground would seem to create an ugly parallel paths problem.
I'd bet that using an autotransformer to derive a neutral on a single phase system is only viable when the neutral is not derived elsewhere, eg a 240V secondary without a center tap, combined with a 120/240V autotransformer to get the neutral. But at this point, why not simply use a secondary with a center tap.
-Jon
