I have found the fastest way to get the moon clips in is to get the cylinder as vertical as possible and grip the moon clip only. Even if the bullets are a little loose in the clip they will hang straight down allowing them to slide in with minimal interference.
What works for me is to line up my middle finger withe the space at 1 o'clock between the holes and drop it in.
The more I practice the more consistent I am.

Larry A.