"Official" grade conversion is skewed at my disadvantage, how to proceed?
As someone who spent several years working in university admissions in the UK, I would suggest that you supply just your Italian transcript to the US university and let them figure out the grade conversions on their own. The US institution should have access to international grade conversion guidelines so it's likely that they'll convert your grades more reasonably than your own university has. 

You might want to consider attaching an official English translation from a professional translation company so they can read the course titles etc. in English. Where I worked, we always asked for official translations in English but never for ECTS equivalents. 

You can supply them with the supplement (and an explanation) later if they ask specifically for that.