I have never seen a transformer (or other device) that will do what you are asking.
That is, to split a single 110 source into two 110 phases with 120 degrees of seperation of the two phases. (Or split a 220 single phase into two 110 phases with 120 degrees of phase seperation.)
Perhaps someone else has, if so, I am interested in hearing about it.
Otherwise, I think you were mislead by someone who did not fully understand what you were asking.
As far as I know, you will have to go back to the idea of two 110 inverters that are piggy backed.
Oso