The scenario is designed so you release as soon as you are pointing down, ie, one half rotation after the scenario starts. If you wait an orbit, you will miss the plane of the moon.I'm still experimenting with the timing of the release. Anywhere on the low side of the flinger's orbit will toss you out to the moon's orbit, it's just a question of how close the moon is when you get there. Do you have any suggestions? When the scenario starts, the flinger is already slightly past its Pe. Is it better to release as soon as you're pointing down, or wait an orbit until you're at or on the other side of Pe?
My technique is to jump into the DG, load up AttitudeMFD in Velocity mode and wait until you pitch is +90.0 then release (Ctrl-D). To get the release accurate, set your MFD update frequency to 0.1sec and slow down time accel to 0.1x when you get to about +87deg.
I have tweaked the scenario so that you can get a direct hit on the moon (see below). Also see image of me passing 12km over the moon after only a single 6.6m/s mid-course burn (to stop me hitting the surface!).