There is cheaper way - directly from moon to probe's orbit, without going far away.
Yeah, I thought about that afterwards. My original reasoning was based on a bi-elliptic transfer: the higher you go, the cheaper it is. But rising my apogee with the gravity assist also raised my perigee, that's were I made a mistake, I could have saved a few percents here. A second gravity assist could have helped a little more otherwise. Well, that was a first try.
And Spock gif is super nice and very fitting!
Haha, a good illustration for a great moment