AA essentially never gives out status matches. When they do, it's to very big spenders. For the rest of us, they offer "Challenges" as a fast track to status based on 90 days of flying. More info on them in this thread in the AA forum, though I doubt they'd be of much use to you.

The suggestions to get a one-day Admiral's Club pass are surely meant well, but they won't do you and your GF much good in Europe. There are only two on the entire continent, at LHR and CDG, and you have to be departing from there.

If you have time, I'd look into credit cards like Diners Club and AmEx Platinum that giv airport lounge access. Of those, DC is by far the easier to get. (The only AmEx card that works is real AmEx Platinum, not the platinum-colored and platinum-branded AmEx-issued cards affiliated with Delta, Hilton, etc., etc. If it doesn't have an annual fee well up in three figures, it's the wrong AmEx Platinum card.)