This isn't really "stacking" as the term is commonly used. With exposure stacking, all the member images are aligned together, and then mathematically combined to decrease noise, and increase resolution or brightness of specific objects. In focus stacking, the in-focus parts are combined from the member images to get the entire subject into focus.
What you want to do is just to combine a number of images so that the main subject movement shows with a stroboscopic-like effect.
I'd suggest using the Gimp and compositing the images with layer masks to bring in just the moon from each shot. The Gimp is an open source analog to Photoshop, and its usage is very very broad and deep, and there's no easy way to encompass a description of everything it can do easily.
The other tool you may want to consider is Hugin. Hugin is primarily used as a panorama stitcher, to combine images, but if you load up all your member images, align them, and use the masking feature to make sure the moon is included from each shot, and then "stitch", you should get a "clone" shot that includes all the moon positions.