All the circuits below need input and output fusing. This is not shown, but absolutely necessary for fire safety.
A 110->220V autotransformer of course provides a split phase output, but the output is not always ground-referenced, and thus you can't use it unless you're careful. In a split-phase supply, the center tap is neutral and bonded to ground. You can get that in an auto-transformer, as long as the central tap is connected to Neutral.

simulate this circuit – Schematic created using CircuitLab
In the schematic above, disregard the dummy primary winding of the transformer - CircuitLab doesn't have an auto-transformer symbol.
As long as the central tap is connected to neutral, LIVE2 is 180 degrees out of phase with LIVE, and thus you have a split-phase supply:

I've looked at industrial isolation transformers with this capability and they are VERY expensive.
Not really. For a fully isolated split-phase supply, you need is two standard 120V-120V isolation transformers, connected as follows:

simulate this circuit
If all you want is to add a split phase to an existing supply, just one 1:1 isolation transformer does it. It has the same amount of wire as an autotransformer, and should cost about the same.

simulate this circuit
VERY expensive
relevant to the question? \$\endgroup\$