First of all, my best wishes to your girlfriend on her birthday. Second, my best wishes to her parents for sporting what promises to be a marvelous night on the town.
My suggestion is to plan on dinner at Chloelys and because this is indeed a special night, not to simply order from the menu but to phone even now and to talk with chef Victor Gluger (considering the birthday involved, feel free to mention to whomever answers the phone that I suggested that you speak with him personally).
Do tell him of the occasion and be sure to discuss the special culinary likes and dislikes of both yourself and your girlfriend and ask him to design a menu for your evening. Considering your girlfriend's passion for cheeses, be sure to mention this to him. Do not ask what actual dishes he will be serving. Sometimes throwing yourself on the mercy of a chef (especially one with the talent, the sense of humor, the romanticism and the creativity that Gluger has) can be the very "best way to go" and the surprises that await can contribute hugely to the pleasure of the meal.
If money is truly of no object, ask him to consult with his sommelier and to select those wines that are considered best matches to the dishes he selects for you. Do, however, consider setting a limit on the cost of the wines as the restaurant has some truly superb wines at truly superb prices and I doubt that your girlfriend's parents are going to be all that generous.
I suggest Chloelys because in addition to being (in my opinion) the very best restaurant in the country at this stage, the atmosphere and the service are absolute delights. If you do go along with this, I hold you responsible for reporting back on the dinner. Anything that should transpire before or after the dinner is, of course entirely your own affair.