It is conceivable that the assembly could be constructed with listed/labeled components, and prior to energization [besides the equipment-grounding conductor carried with the ungrounded 600V supply conductors] could conceivably be tied to "nearest effectively ground building steel"—similar to a fixed installation. It is likely that the grounding lead could be treated effectively the same as the grounding connection of a 600V portable welder.
For that purpose, what about using 6AWG welding cable with an rugged, attached portable clamp, like http://www.thermadyne.com/evolution/bigimage.asp?div=twe&pdtid=285
for secondary and enclosure grounding? As an alternative to extending 208/120V from a remote location, I believe it could function as a safer arrangement.
As an alternate to a 2-winding transformer, if it could be assured to be served from a 4-wire 600Y/347V circuit, an autotransformer arrangement may be practical, obviating the need for the secondary grounding as with a separately derived system. Using an otherwise-rated set of 240/120V transformers with a stock 5% tap, the two-winding 228:120V ratio could be configured as a set of 347:120V autotransformers.