To me, the right way to follow up is personally with one of the individuals you met during the interview process...i.e. in the context of professional networking rather than a job search. Networking provides value to the other party because networking is a two way street. "Give me feedback" is one way, all about you, and work for the other person. It is also risk because the reason companies in the US don't provide feedback is to limit the risk of being sued.
To put it in context, be ok with not getting hired this time (yeah I know it sucks). But the long term is about relationships. Asking for feedback for a position creates a context in which someone is unlikely to say, "I know this other company that's hiring and <important person at other company> is a friend/customer/acquaintance of mine. Here is their contact information."
I'd put it this way, if someone gave you the impression that it is a good idea to ask for feedback following an interview in the US, that is an impression to remove from your mind. It raises the concern that you might want to argue over the feedback. If a company interviews six people for a position, most or all of them won't get hired.
One way to work the networking side is simply to try to connect on Linkedin the next day as follow up. It's low effort on the other person's part to open the door to future interaction while allowing them to signal that they are not interested in a passive, non-confrontational way or carefully consider their response.
Good luck.