"can only reach an elliptical Geosynchronous Transfer Orbit"
Once you're in Earth orbit, you're halfway to just about anywhere. From geosynchronous orbit It's only a small bit of ΔV to the Moon. As a matter of fact, Huges saved Asiasat 3 by by using a Lunar gravity assist when the Russian Proton booster malfunctioned. It did an Apollo 8 style figure 8 around the Moon.