Based on your making this computation, I infer the equipment is 2-wire single phase, which I don't believe has otherwise been indicated. The rest of my response is predicated on that being the case:
You can't use an autotransformer from a 480V system to get 2-wire 240V unless the 480V system is corner grounded and one of the circuit conductors is the grounded conductor. See 210.9 and 215.11.
But with a 2-wire primary / 2-wire secondary isolation transformer, my impression is that the various relevant NEC sections have language that basically allow you to treat the secondary conductors as protected by the primary OCPD with the appropriate ratio (have not double checked that statement).
E.g. if the equipment is fine with a 30A 240V circuit (ignoring the 220V question, which you could use an autotransformer for if necessary), then a suitable transformer supplied by a 15A 480V breaker would be fine load-wise, with the secondary conductors sized for 30A.
Except that the transformer primary OCPD size would be determined by sizing it large enough to avoid inrush tripping. In which case the primary conductors would end up larger than necessary for the load. And it might be useful to use secondary OCPD just to avoid oversizing of the secondary conductors.
Lastly, the above is just inference from reading here in this forum, so hopefully if I got any of the details wrong, I will be corrected. : - )
Cheers, Wayne
