Are you ready for a long slow process? (It will get quicker as you get more practice at it and 300 images is plenty of practice

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Open a fully eclipsed image as your master and create a copy of it. Close the master and rename the copy "animation control" just so you know which one it is. Crop it to the size you want. Now make a copy of it. Open your first image and using your move tool drag and drop the first image onto the "animation control" COPY!! In your layers blending option select "Difference" and use your move tool until the the top layer block out the corresponding section of the bottom layer. You will get the idea after mucking around with it. You may also have to use the Edit>Transform>rotate option as well if you need to rotate the top layer.
Once you have it to your satisfaction return the layer blending option to normal. And now flatten. You should have an image with the same crop size as your "animation control" with the moon correctly lined up.
Now save as "Animation Image 1"
Repeat: Duplicate "animation control" Open second image, drag and drop onto "animation control copy", Difference blending and align, Difference blending normal, Flatten, Save As "Animation Image 2"
Once you have completed this process, and yes it will take a while but will look great when you finished, you can use a free animation program like Advanced Gif Animator to create your animation. Beware: it will be very large in megs.
Btw, when you are cropping your original, play around with it for a while to get a good size. It's not much fun when you are half way through your aligning and realize you should have made each frame with more or less "black space"