For the most part, a three phase machine can run well off a phase converter. Transformer welding machines are not as sensitive as many different CNC equipment to voltage differentiations when using a phase converter. Inverters may be a problem, but with their superior line conditioning, I'm sure they will run fine as well.
Keep in mind, too, that a rotary type phase converter is the only one that will handle transformer type loads.
Static type converters often use a capacitor network to induce a phase shift for starting motor type loads. After starting, statics make the motor run in a "single phasing" mode, ie, only two of the three hot wires are providing power to the motor. This is why we are very careful about motor horsepower and derate many motors hooked up on a static phase converter.
Rotary converters are easily built from common parts. You can go to Rotophase or similar companies, but the cost from them is somewhat high.
Simple converters can be fabricated easily. Email direct for more details.There are many plans available from the internet as well.
BTW-the power from a rotary converter is, indeed, true three phase power, from what I can see.
Hope this helps some...
Good Luck
brande