These matters are always best addressed at the time. Making a scene isn’t necessary. A quiet word with the manager, away from your girlfriend if you feel you need to be protective of her, normally sorts it out.

Your point about being young and flying a cash First fare I don’t think is relevant. Do the staff even know whether you’re a First customer, or a gold guest list on a cheap European tier point run or an even cheaper domestic economy hop?

What is it you actually want? You’ve said you don’t want a boiler plate response. If you are seeking to ensure service improvement happens next time, by all means write in. Would a personalised response and apology be satisfactory or are you seeking some form of compensation? If the latter, what would meet your expectation to resolve the issue? In my view though, having failed to address the issue and therefore not giving the staff a chance to rectify problem, I really don’t believe compensation is due in this situation.